Question

Problem 4: Beats Two musicians are playing the same instruments. The first one emits the sound with correct wavelengtlh 58 cm while the second one is off, and the wavelength is 5 mm longer. a) What is the frequency of the beats when they play together? b) By how much does the second musician need to change her instrument's wavelength so that the frequency of the beats is reduced to 1 Hz?

Answer 1

we know the formula

f=v/$\lambda$

$\lambda$1=58cm

2=58.5cm

a) so f1=34400cm/s/58=593.1Hz

f2=34400cm/s/58.5=588.2Hz

so fbeat=f1-f2=593.1-588.2=5Hz

so answer is 5Hz

b) here we have

f1-f2= f beat

593-f2=1

f2=592.1Hz

so new wavlength

$\lambda$=34400cm/s/592.1=58.1cm

so the second musician should change the wavelength of her instruments by 4mm to 58.1 cm