Wavespeed in a Vibrating String

In summary, the conversation was about a tuning fork mounted on a ring stand with a string attached to it. A mass was hung at the end of the string and the tuning fork was activated, causing a wave to pass through the string. The question was how many wavelengths or fractions of a wavelength would occupy the string if the mass was replaced with 4 times the original mass. The solution attempted by the person involved using equations to calculate the tension and wavespeed before and after adding the mass, and then using the wavelength equation to find the number of wavelengths. However, the final answer was incorrect and further help was requested.
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Homework Statement


A tuning fork, frequency 388Hz, is mounted vertically on a ring stand. A string of length 2m is attached to the tuning fork, and a mass m is hung at the end of the string. The tuning fork is activated, and a wave passes through the string (wavespeed 600m/s.) Assume the tension does not affect the frequency.

If mass m is replaced with mass 4m, how many wavelengths, or fractions of a wavelength, occupy the string?

Homework Equations


wavelength= velocity/frequency
wavespeed= sqrt[tension/(mass/length)] in a vibrating string


The Attempt at a Solution


Ok, so I used the second equation to isolate T before more mass was added, assuming m=1kg. I found the tension, and it was 1800N. Then I found the wavespeed after the mass was added. Since the mass increased by a factor of 4, I used 7200N as the tension and 4kg as the mass. I found the velocity to be 60m/s. Then I used the first equation to find the wavelength, 0.15m approx. Then I divided 2 by that to find how many whole waves would occupy the string, which was 13, and apparently that is wrong.

I am not sure what I am doing wrong, thanks for helping.
 
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Related to Wavespeed in a Vibrating String

1. What is the formula for calculating the wavespeed in a vibrating string?

The formula for calculating the wavespeed in a vibrating string is:
c = √(T/µ)
Where c is the wavespeed, T is the tension in the string, and µ is the linear density of the string.

2. How does tension affect the wavespeed in a vibrating string?

An increase in tension in the string will result in a higher wavespeed, while a decrease in tension will result in a lower wavespeed. This is because tension is directly proportional to the wavespeed according to the formula c = √(T/µ).

3. How does the linear density of the string affect the wavespeed?

The wavespeed is inversely proportional to the linear density of the string. This means that a higher linear density will result in a lower wavespeed, while a lower linear density will result in a higher wavespeed. This can be seen in the wavespeed formula c = √(T/µ), where the square root of µ is in the denominator.

4. Does the wavespeed in a vibrating string depend on the frequency of the vibration?

No, the wavespeed in a vibrating string is independent of the frequency of the vibration. This means that no matter how fast or slow the string is vibrating, the wavespeed will remain constant as long as the tension and linear density of the string do not change.

5. How can the wavespeed in a vibrating string be measured experimentally?

The wavespeed in a vibrating string can be measured experimentally using a stroboscope or a laser and a photodiode. The stroboscope or laser is used to create a stationary wave on the string, while the photodiode measures the wavelength. The wavespeed can then be calculated by dividing the wavelength by the period of the vibration.

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