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Q.

Two wires are fixed in a sonometer. Their tensions are in the ratio 8 : 1. The lengths are in the ratio 36 : 35. The diameters are in the ratio 4 : 1. Densities of the materials are in the ratio 1 : 2. If the higher frequency in the setting is 360 Hz, the beat frequency when the two wires are sounded together is

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a

10

b

6

c

8

d

5

answer is A.

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Detailed Solution

Let I, d, f, p and p be the length, diameter, tension, density (mass per unit length] and number of loops of sonometer wire respectively. The frequency n of a stretched string is given byn=pLdTρ or n∝1LdTρ n1n2=T1ρ2T2ρ1×L2L1×d2d1 =8121×3536×14=0⋅972  Now n2360=0⋅972 or n2=350 Beat frequency =360 -350 =10
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