A harpsichord string of length 1.50 m and linear mass density 26.0 mg/m vibrates at a (fundamental) frequency of 460.0 Hz.

(a) What is the speed of the transverse string waves?
m/s

(b) What is the tension?
N

(c) What are the wavelength and frequency of the sound wave in air produced by vibration of the string? The speed of sound in air at room temperature is 340 m/s.
wavelength m
frequency Hz

Please help; I have no idea on how to do this one.

No idea? YOu misses lectures or something.

a) waveequation> freq*3m= speedwave
b) v= sqrt (2Tension/(mass/length)) you can solve for tension.

in air,
c) frequency*wavelenght= speed in air
you were given frequency, calculate wavelength.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html

Thank you! I got the other parts, but I still cant get part b. Isn't it sqrt(26/1.5) and the answer multiplied by 2 to get tension, but its giving me wrong. I don't know why!

To solve this problem, we need to use the wave equation:

v = fλ

where:
v is the speed of the wave
f is the frequency of the wave
λ is the wavelength of the wave

(a) To find the speed of the transverse string waves, we need to calculate the wavelength of the wave using the given information. Then, we can use the wave equation to find the speed.

Given:
Length of the string, L = 1.50 m
Linear mass density, μ = 26.0 mg/m = 0.026 kg/m
Frequency of the wave, f = 460.0 Hz

First, let's calculate the wavelength (λ) of the wave on the string:
λ = 2L

λ = 2 * 1.50 m = 3.00 m

Now, we can calculate the speed (v) using the wave equation:
v = fλ
v = (460.0 Hz) * (3.00 m)

v = 1380 m/s

Therefore, the speed of the transverse string waves is 1380 m/s.

(b) To find the tension in the string, we can use the formula:

T = μv²

where:
T is the tension in the string
μ is the linear mass density of the string
v is the speed of the transverse string waves (already calculated to be 1380 m/s)

Given:
Linear mass density, μ = 26.0 mg/m = 0.026 kg/m
Speed of the transverse string waves, v = 1380 m/s

T = (0.026 kg/m) * (1380 m/s)²

T = 0.026 kg/m * 1904400 m²/s²

T = 494.664 N

Therefore, the tension in the string is approximately 494.664 N.

(c) To find the wavelength and frequency of the sound wave in air produced by vibration of the string, we already know the speed of sound in air (v = 340 m/s).

Given:
Speed of sound in air, v = 340 m/s

We can use the equation:
v = fλ

To find the wavelength (λ), we rearrange the equation:
λ = v / f

λ = 340 m/s / 460.0 Hz

λ = 0.739 m

Therefore, the wavelength of the sound wave produced by the vibrating string is approximately 0.739 m.

The frequency (f) of the sound wave is the same as the frequency of the vibrating string, which is given as 460.0 Hz.

Therefore, the frequency of the sound wave in air is 460.0 Hz.

To find the answers to these questions, you'll need to use the appropriate formulas and equations related to waves, string vibrations, and sound waves.

(a) The speed of transverse waves on a string is given by the equation:

v = √(T/μ)

where v is the speed of the wave, T is the tension in the string, and μ is the linear mass density of the string.

In this case, you are given the linear mass density (26.0 mg/m) and the fundamental frequency (460.0 Hz), but you need to find the speed of the wave, so rearrange the equation to solve for v:

v = √(T/μ)

We don't have the tension (T) directly, so we need to find it using the fundamental frequency:

f = (1/2L) * √(T/μ), where L is the length of the string and f is the fundamental frequency.

Rearranging this equation for T:

T = (4μL^2 * f^2)

Now you can substitute the given values and solve for T, and then plug the values of T and μ into the equation for v to calculate the speed.

(b) To find the tension (T), use the equation T = (4μL^2 * f^2) from the previous step. Substitute the given values (μ, L, and f) into this equation and evaluate to find the tension.

(c) To find the wavelength (λ) and frequency (f) of the sound wave produced by the vibrating string, you can use the equation for the speed of a wave (v), which is given by:

v = f * λ

Given the speed of sound in air (340 m/s), you can rearrange this equation to solve for λ:

λ = v / f

Substitute the values of v and f to find the wavelength.

Now that you understand the steps and equations involved, you can proceed to calculate the answers using the given values.