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1. ⇒  (MHT CET 2023 12th May Morning Shift )

41 tuning forks are arranged in increasing order of frequency such that each produces 5 beats/second with next tuning fork. If frequency of last tuning fork is double that of frequency of first fork. Then frequency of first and last fork is

A. 400 , 200   Hz

B. 200 , 400   Hz

C. 100 , 200   Hz

D. 205 , 410   Hz

Correct Option is (B)

Let Frequency of 1 st  tuning fork be = n 1

frequency of 41 st  tuning fork = n 41

Now,

n 41 = n 1 + ( 41 1 ) × 5  But,  n 41 = 2 n 1 2 n 1 = n 1 + 200 n 1 = 200   Hz n 41 = 400   Hz

2. ⇒  (MHT CET 2021 20th September Evening Shift )

Beats are produced by waves y 1 = a sin 2000 π t and y 2 = a sin 2008 π t . The number of beats heard per second is

A. 4

B. 1

C. zero

D. 8

Correct Option is (A)

y 1 = a sin 2000 π t 2 π n 1 = 2000 π n 1 = 1000   Hz

y 2 = a sin 2008 π t 2 π n 2 = 2008 π n 2 = 1004   Hz  Beat frequency  = n 2 n 1 = 4   Hz

3. ⇒  (MHT CET 2021 20th September Morning Shift )

The frequencies of three tuning forks A , B and C are related as n A > n B > n C . When the forks A and B are sounded together, the number of beats produced per second is ' n 1 '. When forks A and C are sounded together the number of beats produced per second is ' n 2 '. How may beats are produced per second when forks B and C are sounded together?

A. n 1 n 2

B. n 1 + n 2 2

C. n 2 n 1

D. n 1 + n 2

Correct Option is (C)

n A n B = n 1 ..... (i)

n A n C = n 2 ..... (ii)

Subtracting Eq. (ii) from Eq. (i)

n C n B = n 1 n 2

or n B n C = n 2 n 1