Question icon
Grade Upto college level Engineering Entrance Exams

A tuning fork vibrating with a sonometer having 20 cm wire produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to 2 l cm. the frequency of the tuning fork (in Hz) must be (a) 200 (b) 210 (c) 205 (d) 215

Profile image of sumit kumar
12 Years agoGrade Upto college level
Answers icon

2 Answers

Profile image of Arun
6 Years ago
Fundamental frequency is:
n = 1/2l √T/m
n 1/l
assume for 20cm frequency is n1
and for 21 cm frequency is n2
So
n1/n2 = 21/20
then n1 = 21x and n2 = 20x
Let frequency nf for producing 5 beats so n1 > nf > n2
So n1 - nf = 5
21x - nf = 5 ....(i)
And nf - n2 = 5
nf - 20x = 5 .....(ii)
from (1) ans (2) we get x = 205 hz
Profile image of Vikas TU
6 Years ago
 
Let the frequency of tuning fork be N
As the frequency of vibration string∝1 / length of string For sonometer wire of length 20cm,frequency must be (N+5) and that for the sonometer wire of length 21 cm, the frequency must be (N−5) as in each case the tuning fork produces 5 beats/sec with sonometer wire.
Hence n1I1=n2I2
⇒(N+5)×20=(N−5)×21
⇒N=205Hz

question mark
Hello,
 
Can we learn and prepare for MHT-CET online ?
engineering entrance exams

Last Activity: 4 Years ago