Question:

A string of length 2.0 m is held under a tension of 200 N. The string is fixed at both ends and is vibrating in its second harmonic. The mass of the string is 0.02 kg. A set of interfering waves produced on this string causes a standing wave pattern to form.

a) Calculate the speed of the waves on the string. b) Calculate the frequency of the waves. c) Determine the wavelength of the waves on the string.

Give your answers to three significant figures.

Answer:

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

Where: $v$ = speed of waves $T$ = tension in the string $\mu$ = mass per unit length of the string

Plugging in the given values:

Therefore, the speed of the waves on the string is 100 m/s.

b) The frequency of a wave can be calculated using the equation:

Where: $f$ = frequency of the wave $v$ = speed of the wave $L$ = length of the string

Since the string is vibrating in its second harmonic, the length of the string ($L$) is equal to half of the wavelength. Thus, the frequency can be calculated as:

Therefore, the frequency of the waves is 25 Hz.

c) The wavelength of the standing wave on the string can be determined using the equation:

Where: $\lambda$ = wavelength of the wave $L$ = length of the string $n$ = harmonic number (in this case, 2 for the second harmonic)

Plugging in the given values:

Therefore, the wavelength of the waves on the string is 2.0 m.

In conclusion, the speed of the waves on the string is 100 m/s, the frequency of the waves is 25 Hz, and the wavelength of the waves is 2.0 m.

This requires an understanding of the fundamental concepts related to standing waves and interference, as well as the application of relevant equations.