What are the three longest wavelengths for standing waves on a 240 cm long string that...

What are the three longest wavelengths for standing waves on a 240 cm long string that is fixed at both ends?

If the frequency of the second-longest wavelength is 50.0 Hz, what is the frequency of the third-longest wavelength?

Solutions

Expert Solution

For a standing wave if both ends are fixed, the wavelength must be such that the length of the string must be an exact multiple of half a wavelength.

The longest wavelength must be such that the length of the string must be equal to half a wavelength, and therefore the wavelength must be double the length of the string, or 2*240 cm = 480 cm.

The second longest wavelength must be such that the length of the string must be equal to a whole wavelength, so the second longest wavelength must be 240 cm.

The third longest wavelength must be such that the length of the string must be equal to 1.5 times the wavelength, so the wavelength must be 240cm/1.5 = 160 cm.

The speed is the same for all standing waves. And remember v = f?, speed is frequency times wavelength. The speed of the third longest wavelength is the same as the speed of the second longest wavelength, which is

v = f? = (50.0 Hz)(2.4 m) = 120 m/s, and dividing by the wavelength of the third-longest (1.6 m), gives a frequency of =75 Hz.

genius_generous answered 1 year ago

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