1. (JEE Main 2020 (Online) 5th September Morning Slot)

Assume that the displacement(s) of air is proportional to the pressure difference ( $Δ$ p) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ( $ρ$ ) and the frequency (f). If $Δ$ p ~ 10 Pa, v ~ 300 m/s, $ρ$ ~ 1 kg/m³ and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1) :

A. 1 mm

B. $\frac{3}{100}$ mm

C. 10 mm

D. $\frac{1}{10}$ mm

Correct Answer is Option (B)

Given, S $\propto$ $Δ$ p

and Proportionally constant = 1

We know,

$Δ$ p = S $β$ k

= $ρ$ v² $\times$ $\frac{ω}{v} \times S$

= $ρ v ω S$

$∴$ S = $\frac{Δ p}{ρ v ω}$

= $\frac{Δ p}{ρ v 2 π f}$

= $\frac{Δ p}{ρ v f}$

[As Proportionally constant = 1 so assume 2 $π$ = 1]

$= \frac{10}{1 \times 300 \times 1000}$

$= \frac{1}{30} m m$

$\approx \frac{3}{100} m m$

2. (JEE Main 2019 (Online) 9th April Morning Slot)

The pressure wave, P = 0.01 sin [1000t – 3x] Nm^–2, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0°C. On some other day, when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336 ms^–1 . Approximate value of T is :

A. 12°C

B. 15°C

C. 4°C

D. 11°C

Correct Answer is Option (C)

Speed of wave from wave equation

$v = - \frac{(c o e f f e c i e n t o f t)}{(c o e f f e c i e n t o f x)}$

$v = - \frac{1000}{(- 3)} = \frac{1000}{3}$

Since speed of wave $\propto \sqrt{T}$

So $= \frac{1000}{\frac{3}{336}} = \sqrt{\frac{273}{T}}$

$\Rightarrow$ T = 277.41 K

T = 4.41°C

3. (AIEEE 2002)

When temperature increases, the frequency of a tuning fork

A. increases

B. decreases

C. remains same

D. increases or decreases depending on the material

Correct Answer is Option (B)

KEY CONCEPT : The frequency of a tuning fork is given by the expression

$f = \frac{m^{2} k}{4 \sqrt{3} π ℓ^{2}} \sqrt{\frac{Y}{ρ}}$

As temperature increases, $ℓ$ increases and therefore $f$ decreases.

Waves