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A sonometer string and a tuning fork when sounded together gives 6 beats/sec, whether the length of sonometer string is 85 cm or 100 cm. the frequency of tuning fork is (a) 262 Hz (b) 256 Hz (c) 260 Hz (d) 234 Hz

A sonometer string and a tuning fork when sounded together gives 6 beats/sec, whether the length of sonometer string is 85 cm or 100 cm. the frequency of tuning fork is
(a) 262 Hz
(b) 256 Hz
(c) 260 Hz
(d) 234 Hz

Grade:Upto college level

2 Answers

Arun
25758 Points
2 years ago
Probable frequencies of tuning fork be 
n+4
 or 
n4
                    Frequency of sonometer wire 
n1l
                    
n+4n4=10095
 or 
95(n+4)=100(n4)
                    or 
95n+380=100n400
 or 
5n=780
 or 
n=156

 
Vikas TU
14149 Points
2 years ago
Letn = Frequency of the tuning fork
n1=Frequency of the wire corresponding to length of L1 (39.5 cm)
n2=Frequency of the wire corresponding to length of L2 (40.5 cm)
The frequency of wire is inversely proportional to its length
Hence,n1>n2
So, n1/n2=n+4 / n−4 [ since number of beats = 4]
But, n1/n2=L2/L1
n+4 / n−4 = 40.5/39.5
40.5n−162=39.5n+158
n=320 HzAns:Frequency of the tuning fork=320 Hz

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