Question

One of the 57.5cm -long strings of an ordinary guitar is tuned to produce the note B3(frequency 245 Hz) when vibrating in its fundamental mode.

1. Find the speed of transverse waves on this string.

2. If the speed of sound in the surrounding air is 344 m/s, find the frequency of the sound wave produced in the air by the vibration of the B3 string.

3. If the speed of sound in the surrounding air is 344 m/s, find the wavelength of the sound wave produced in the air by the vibration of the B3 string.

Answer 1

f= n*v/(2L) ; n=1 as it is fundamnetal mode.

1) v= 245*2*0.575 = 281.75m/s.

2) frequency will be the same = 245Hz.

3) wavelength = v/f= 344/245 = 1.4041 m

Answer 2

Speed=wavelength*freequency

so

ans 1 assuming node at centre so wavelength= l-2

so speed= .57.5/2*245= 70.4375 m/s

ans 2 344/.575= 596.52 hz

ans 3 344/245 = 1.4 approx 140cm