Suppose l₁= first resonance length and l₂ being second resonance length. Also, v0 and v27 being velocity at 0Cand27Crespectively.

First resonance length (l1) = 17 cm = 0.17 m
Second resonance length (l2) = 52.6 cm = 0.526 m
Frequency of the tuning fork (f) = 512 Hz

At 27C,

v₂₇ = 2f(l2-l1)

= 2 x 512(0.526-0.17)

= 364.5 m/s

We know vT,

Also, End correction (c) =

The frequency of sound produced in an air column is inversely proportional to the length of the air column. As the level of water in the vessel increases, the lengthof air column above it decreases. Hence, the frequency of sound produced goes on increasing.

Thefrequencyof transverse vibration of astretched stringis calculated as

where;

• T is the tension on the string
• μ is the mass per unit length

When thetensionis halved and theareaof cross section isdoubled, we calculate the frequencyas;

Thus, when thetensionis halved and theareaof cross section isdoubled, thefrequencyincreases by a factor of1.414.

The drawback of Newton's formula for velocity of sound are:
1. The velocity of sound calculated from Newton's formula is279.9 m/s at N.T.P. Experimentally, they found that the velocity of sound in air at N. T. P is 332 m/s. Thus, there is a considerable difference between the value predicted by Newton’s formula and the experimental value.

2. Experimental value is 16% greater than the value given by the formula. Newton failed to satisfactorily explain the difference.

Laplace Correction:

Newton...

Time taken (t) = 3 sec
Velocity of sound (v) = 332 m/s
Distance travelled (d) = ?

We know,

d = v x t = 332 x 3 = 996 m

Hence, the source of thunder is about 996 m far from the boy.

The lower the density, the faster sound travels in a medium. The density of water vapour is less than that of air. So the density of air mixed with water vapour is less than that of dry air. Hence the speed of sound in moist air is greater than that in dry air(v1/ρ) . However, the density of water vapour is more than that of hydrogen, so the density of moist hydrogen is more than that of dry hydrogen. Consequently, the speed of sound in moist hydrogen is less than that in dry hydrogen.

The lower the density, the faster sound travels in a medium. The density of water vapour is less than that of air. So the density of air mixed with water vapour is less than that of dry air. Hence the speed of sound in moist air is greater than that in dry air(v1/ρ) . However, the density of water vapour is more than that of hydrogen, so the density of moist hydrogen is more than that of dry hydrogen. Consequently, the speed of sound in moist hydrogen is less than that in dry hydrogen.