okay the question i got was asking the lengths of the first, second, and third waves of a standing wave, of a string that is fixed at both ends. the strings length is 2.38 meters. Ive already figured out the three lengths, being 4.76, 2.38, and then 1.59. how would i figure out the frequency of the third wavelength, if the second is 54Hz???

if the wavelength is half and the speed of the wave is constant then the frequency is double.

distance = rate * time
wavelength = speed * period
period = 1/frequency
so
wavelength = speed /frequency

thanks, that helped a lot!

To figure out the frequency of the third wavelength, we need to use the formula for the speed of a wave on a string:

v = λ * f

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

In this case, we know the second wavelength (λ₂ = 2.38 m) and its corresponding frequency (f₂ = 54 Hz). Let's rearrange the formula to solve for v:

v = λ₂ * f₂

Now, we can use this value of v to find the frequency of the third wavelength (f₃ = ?). We know the third wavelength (λ₃ = 1.59 m), so we can rearrange the formula again to solve for f₃:

f₃ = v / λ₃

To solve the problem, plug in the values we have:

v = λ₂ * f₂
= 2.38 m * 54 Hz
= 128.52 m/s

Now, use this value of v to find f₃:

f₃ = v / λ₃
= 128.52 m/s / 1.59 m
= 80.8 Hz

Therefore, the frequency of the third wavelength is approximately 80.8 Hz.