Frequency on Waves and Tension Quick Question

In summary, the piano tuner is hearing three beats every two seconds when two piano strings are supposed to be vibrating at 128 Hz. This means that the difference between their frequencies is 1.5. To bring them in tune, the tension must be increased or decreased by a certain percentage. Using equations for velocity and wavelength, the frequency can be expressed as a function of tension. By knowing the relative change in frequency, the relative change in tension can be calculated. Additionally, a trig identity can be used to find the difference between the two frequencies if the beat frequency and one of the frequencies is known.
  • #1
isisfierce
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1. Two piano strings are supposed to be vibrating at 128 Hz, but a piano tuner hear three beats every 2 seconds when they're played together

a) If one is vibrating at 128 Hz, what must be the difference between their frequencies?
Answer - 3 Beats Per Two Seconds, Frequency Diff = 1.5

b) By how much in percent must the tension be increased or decreased to bring them in tune?

-- B is where I'm stuck on. I have the two equations v= lambda x frequency and
velocity = sqrt ( Tension / mass per length )

So I set both of them equal to each other and found that the Tension is proportional to the Frequency Squared?? I'm not sure if this is the right direction :( And if it is I tried putting in the number percent but it didn't work ( Sqrt 1.5 )
 
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=] Bump!
 
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another bump!
 
  • #4
You have standing waves in the string. The wavelength is determined by the length of the string.
L= n (lambda/2) if it's fixed at both ends.

lambda= v/f and use v=sqrt(T/linear density)

solve these to get frequency as a function of T .

You know the relative change in frequency (1.5/128) so you can calculate the relative change in tension.
 
  • #5
There is an equation that shows how the "beat" frequencies occur. If you've got two sine waves, sin(A) and sin(B), and A is different from B, there's a trig identity that allows you to add them together and find sin(A + B). If you know the beat frequency and A, you can find B.
 

1. What is the relationship between frequency and wavelength on a wave?

The frequency of a wave is directly proportional to its wavelength. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation: v = fλ, where v is the velocity of the wave, f is the frequency, and λ is the wavelength.

2. How does tension affect the frequency of a wave?

Tension refers to the force applied to a medium that causes a wave to propagate. The higher the tension, the faster the wave will travel, resulting in an increase in frequency. This can be seen in musical instruments, where the tension on strings can be adjusted to produce different frequencies and pitches.

3. What is the difference between a high frequency and a low frequency wave?

A high frequency wave has a shorter wavelength and more cycles per second compared to a low frequency wave. This means that a high frequency wave will have a higher pitch or tone, while a low frequency wave will have a lower pitch or tone.

4. Can the frequency of a wave be changed?

Yes, the frequency of a wave can be changed by altering its wavelength, velocity, or both. This can be achieved by adjusting the tension or properties of the medium through which the wave is propagating, or by using special devices such as filters or amplifiers to manipulate the wave's properties.

5. How is frequency measured and what is the unit of measurement?

Frequency is measured in Hertz (Hz), which is equivalent to one cycle per second. It can be measured using specialized instruments such as an oscilloscope or by counting the number of cycles that occur in a given time period. The higher the frequency, the more cycles that occur in a second.

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