Question

A person is measuring the
velocity of sound in a experiment
He found that velocity of sound
increases by 6lcm/s for every 1 C
Show this mathematically.​

Answer 1

Yes, the  velocity of sound in a experiment increases by 61 cm/s for every 1°C.

Explanation:

v ∝ √T

To covert °C to Kelvin, we get use the below formula:

T (K) = t°C + 273

The velocity of sound at 0°C, we get,

v ∝ √(0 + 273) → (1)

The velocity of sound at t°C, we get,

v₁ ∝ √(t + 273) → (2)

Now, on dividing equation (1) and (2), we get,

v₁/v = √(t + 273)/(0 + 273)

$v_{1}=v\left(1+\frac{t}{273}\right)^{1 / 2}$

$v_1\approx v \left(1+\frac{1}{2} \times \frac{t}{273}\right)$

v₁ = v + (v × t)/546

We know that, the speed of the sound in air at 0°C is:

v = 332 m/s

v₁ - v = (332 × t)/546

v₁ - v ≈ 0.61 × t m/s

When t = 1°C, the speed of the sound is:

v₁ - v ≈ 0.61 m/s = 61 cm/s

Hence it is mathematically proved.