Question

A 80.0 cm wire of mass 7.40 g is tied at both ends and adjusted to a tension of 42.0 N .

When it is vibrating in its second overtone, find the frequency at which it is vibrating.

When it is vibrating in its second overtone, find the wavelength at which it is vibrating.

When it is vibrating in its second overtone, find the frequency of the sound waves it is producing.

When it is vibrating in its second overtone, find the wavelength of the sound waves it is producing.

Answer 1

보 L. 커

Second overtone i.e., third harmonic in string vibration is shown in figure.

Wavelength $\lambda$ = (2/3) L = (2/3) $\times$ 0.8 m = 0.533 m , where L is length of string

Speed v of trasverse wave in string under tension T is given by

T W = = 40 9.25 x 10-3 65.76m

where $\mu$ = m/L is mass m per unit length of string

frequency f of vibration of string is obtained from equation v = f $\lambda$

frequency of vibration f = v / $\lambda$ = 65.76 / 0.533 = 123 Hz.

Frequency of sound wave is same as frequency of string vibration.

If v_s = 340 m/s, is speed of sound then wavelength of sound wave = 340 /123 = 2.764 m

Conclusion :-

When string is vibrating in its second overtone, the frequency at which it is vibrating = 123 Hz

When string is vibrating in its second overtone, wavelength at which it is vibrating = 0.533 m

When string is vibrating in its second overtone, frequency of the sound waves it is producing = 123 Hz

When string is vibrating in its second overtone, wavelength of the sound waves it is producing = 2.764 m