Physics High School

A piano tuner stretches a steel piano wire with a tension of 765 N. The steel wire has a length of 0. 600m and a mass of 4. 50g.

What is the frequency f1 of the string's fundamental mode of vibration?

Express your answer numerically in hertz using three significant figures

Answers

Answer 1

The frequency f₁ of the string's fundamental mode of vibration is approximately 96 Hz, expressed to three significant figures.

The formula used to determine the frequency of a string's fundamental mode of vibration is given by:

f₁ = (1/2L) √(T/μ)

where:

f₁ is the frequency of the string's fundamental mode of vibration

L is the length of the string

T is the tension in the string

μ is the linear mass density of the string

Given values:

L = 0.600 m

T = 765 N

μ = 0.0075 kg/m

By substituting the values into the formula:

f₁ = (1/2L) √(T/μ)

f₁ = (1/2 × 0.600 m) √(765 N/0.0075 kg/m)

f₁ = (0.300 m) √(102000 N/m²)

f₁ = (0.300 m) (319.155)

f₁ = 95.746 Hz ≈ 96 Hz

Learn more about string's fundamental mode  here:-

https://brainly.com/question/29725169

#SPJ11

Related Questions

a racquetball strikes a wall with a speed of 30 m/s and rebounds in the opposite direction with a speed of 1 6 m/s. the collision takes 5 0 ms. what is the average acceleration (in unit of m/s 2 ) of the ball during the collision with the wall?

Answers

The average acceleration of the racquetball during the collision with the wall is -280 m/s^2.

To find the average acceleration of the racquetball during the collision with the wall, we can use the formula:
Average acceleration = (final velocity - initial velocity) / time

Given that the racquetball strikes the wall with an initial speed of 30 m/s and rebounds with a final speed of 16 m/s, and the collision takes 50 ms (or 0.05 s), we can substitute these values into the formula:
Average acceleration = (16 m/s - 30 m/s) / 0.05 s
Simplifying this equation, we get:

Average acceleration = (-14 m/s) / 0.05 s
Dividing -14 m/s by 0.05 s gives us an average acceleration of -280 m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, which means the ball is decelerating during the collision.
Therefore, the average acceleration of the racquetball during the collision with the wall is -280 m/s^2.
The average acceleration of the racquetball during the collision with the wall can be found using the formula:

average acceleration = (final velocity - initial velocity) / time. Given that the initial speed is 30 m/s, the final speed is 16 m/s, and the collision takes 50 ms (or 0.05 s), we can substitute these values into the formula. By subtracting the initial velocity from the final velocity and dividing by the time, we find that the average acceleration is -280 m/s^2.

The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, meaning the ball is decelerating during the collision.

You can read more about velocity at https://brainly.com/question/80295

#SPJ11

Other Questions
a racquetball strikes a wall with a speed of 30 m/s and rebounds in the opposite direction with a speed of 1 6 m/s. the collision takes 5 0 ms. what is the average acceleration (in unit of m/s 2 ) of the ball during the collision with the wall? For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y=f(x)=x^2+x;x=4,x=1 A compound consisting of carbon and hydrogen consists of 67.90%carbon by mass. If the compound is measure to have a mass of 37.897Mg, how many grams of hydrogen are present in the compound? Explain the steps to generate machine code from a C/C++ code. 0.059 and 0.01 which is greater? Eight guests are invited for dinner. How many ways can they be seated at a dinner table if the table is straight with seats only on one side?A) 1B) 40,320C) 5040D) 362,880 Write the slope -intercept form of the equation of the line containing the point (5,-8) and parallel to 3x-7y=9 We can use JS DOM to add event listeners to elements?true or false the area of the pool was 4x^(2)+3x-10. Given that the depth is 2x-3, what is the wolume of the pool? what is the essential credible commitment problem for rebel groups to lay down their arms for peace? Which of the following are input into the "Define Scope"process?a) The Scope Statementb) The WBSc) Status Reportsd) The project charter Required information [The following information applies to the questions displayed below] The following is financial information describing the six operating segments that make up Fairfield. Inc. (in thousands): Consider the following questions independently. None of the six segments have a primarily financial nature. What volume of revenues must a single customer generate to necessitate disclosing the existence of a major customer? (Enter yc swer in dollars but not in thousands.) The following information applies to the questions displayed below.] The following is financial information describing the six operating segments that make up Fairfleid, inc. (in thousands: Consider the following questions independently. None of the six segments have a primarily financial nature. Now assume each of these six segments has a profit or loss (in thousands) as follows, which warrants separate disclosure? imagine a bank that offers 8% annual earnings on savings accounts.As an avid saver, you decide to put $40 in your savings accountevery month. If the bank requires a $50 deposit to create theaccountImagine a bank that offers 8 % annual earnings on savings accounts. As an av If the bank requires a $ 50 deposit to create the account and interest is compo Let p_{n} be defined as A classified balance sheet involves: Select one: Providing more detailed information regarding a company's existing assets and liabilities Presenting the balance sheet in a specific format, based on the standard by industry Grouping assets and liabilities into current and non-current assets and liabilities Organising the revenue and expense line items from largest to smallest Which of the following is incorrect?A. By comparing TATO and FATO, we know the proportion of currentassetsB. Increasing payable payment period indicates better cashmanagementC. Decreasing receiva You may need to use the appropriate appendix table or technology to answer this question. Fewer young people are driving. In year A, 62.9% of people under 20 years old who were eligible had a driver's license. Twenty years later in year B that percentage had dropped to 42.7%. Suppose these results are based on a random sample of 1,900 people under 20 years old who were eligible to have a driver's license in year A and an year B. (a) At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year A? (Round your answer to four decimal places.) At 95% confidence, what is the interval estimate of the number of eligible people under 20 years old who had a driver's license in year A? (Round your answers to four decimal places.) to (b) At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year B? (Round your answer to four decimal places.) At 95% confidence, what is the interval estimate of the number of eligible people under 20 years old who had a driver's license in year B? (Round your answers to four decimal places.) to (c) Is the margin of error the same in parts (a) and (b)? Why or why not? The margin of error in part (a) is -- Select-- V than the margin of error in part (b). This is because the sample proportion of eligible people under 20 years old whad a driver's license in year B is than the sample proportion of eligible people under 20 years old who had a driver's license in year A. This leads to a -- Select--- interval estimate in part (b). TRUE/FALSE. planning done by top-level managers involves establishing a vision for the company, defining long-term objectives and priorities, determining broad action steps, and allocating resources. a company issued a $500,000, 12 percent, 90-day note payable to acquire an office building. what is the maturity value of the note that the company will pay on the maturity date? group of answer choices Alex is saving to buy a new car. He currently has $800 in his savings account and adds $700 per month. President Lyndon B. Johnson's Great Society is similar to President Franklin D. Roosevelt's New Deal in that both programs ___.