Physics Waves

A wave propagates on a string in the positive $x$ -axis with a velocity $v$ . The shape of string at $t = t_{0}$ is given as $y (x, t_{0}) = A s i n ? (\frac{x}{b})$ . The wave equation for a general time $t$ is:

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Raj Pandey

Contributor-Level 9

$y (x, t_{0}) = A s i n ? (\frac{x}{b})$

$y (x, 0) = A s i n ? (\frac{x + v t_{0}}{b})$

$y (x, t) = A s i n ? (\frac{x + v t_{0} - v t}{b})$

$∴ y (x, t) = A s i n ? [\frac{x - v (t - t_{0})}{b}]$

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a month ago

A sine wave is travelling in a medium. The minimum distance between the two particles, always having same speed, is

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Contributor-Level 10

Particles having phase difference of? will move with same speed.

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a month ago

Two sources of sound emitting sound of nearly equal wavelengths λ₁ and λ₂ are fixed at A and B respectively. A listener moves with velocity u on the perpendicular bisector of line joining A and B. Then the number of beats heard by him per second when it is at distance 2l from A and B, is (Speed of sound = C)

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Contributor-Level 10

θ = 60?
f? = (C - u (√3/2)/λ?
f? = (C - u (√3/2)/λ?
|f? - f? | = | (C - u (√3/2) (1/λ? - 1/λ? )|

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2 months ago

A sound wave of frequency 245 Hz travels with the speed of 300 ms⁻¹ along the positive x-axis. Each point of the wave moves to and for through a total distance of 6 cm. What will be the mathematical expression of this traveling wave?

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alok kumar singh

Contributor-Level 10

The angular frequency ω is calculated as:
ω = 2πf = 2 * 3.14 * 245 = 1.5386 * 10³ rad/s ≈ 1.5 * 10³ rad/s

This continues the solution from number 15 on the previous page.
k = ω / v = (1.53 * 10³) / 300 = 5.1 m? ¹
A = 0.06 / 2 = 0.03m

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2 months ago

Assume that the displacement (s) of air is proportional to the pressure difference (Ap) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ( ρ ) and the frequency (f). If Ap ~ 10 Pa, v ~ 300 m/s, p ~ π11g/m³ and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1)

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alok kumar singh

Contributor-Level 10

B? = µ? I/ (2π (r)
|τ| = |I * l x F|
τ = 2aF
τ = 2 (a) (I) (2a) (µ? I/2πb)
τ = 2µ? I²a²/πb
B on the also equal to B? as
B = µ? I/ (2π√ (b² + a²/4) + µ? I/4
b >>> a
disp = ( kg/ms ²) (s) (m³/kg)
disp = (1) (16) (1/300) (1/1000)
disp in mm = 1000/ (300x100) = 0.03333
⇒ 3/100

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2 months ago

The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is 330 ms⁻¹ :

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Contributor-Level 10

f? = 420 Hz
f? = (V? + V)/ (V? - V) f? = 490
(330 + V)/ (300 - V) 420 = 490
(330 + V)6 = 7 (330 – V)

13 V = 330
V = 33/13 (m/s)
= 91 (km/hr)

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2 months ago

For a transverse wave traveling along a straight line, the distance between two peaks (crests) is $C \to I$ , while the distance between one crest and one trough is $D \to I V$ . The possible wavelengths (in $A \to I V; B \to I$ ) of the waves are:

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Contributor-Level 10

(n) $λ = 5$

$(n, m)$ : Integers

$\begin{array}{r} (\frac{2 m + 1}{2}) λ = \frac{3}{2} \\ \Rightarrow \frac{3 / 2}{5} = \frac{2 m + 1}{2 n} \\ \Rightarrow 3 n = 10 m + 5 \end{array}$

$N, m$ are integers.

So, $m = 1, n = 5, λ = 1$

$\begin{array}{l} m = 4 & n = 15 & λ = \frac{1}{3} \\ m = 7 & n = 25 & λ = \frac{1}{5} \end{array}$

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2 months ago

Two identical strings X and Z made of same material have tension Tₓ and T₂ in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio Tₓ/Tz is:

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alok kumar singh

Contributor-Level 10

f? = 1/ (2l) √ (T? /µ)
f? = 1/ (2l) √ (T? /µ)
f? /f? = 450/300 = √ (T? /T? )
⇒ T? /T? = 9/4 = 2.25

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2 months ago

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 400 Hz $\frac{}{_{}} \frac{}{_{}^{}}$ to 400 Hz $\frac{}{_{}^{}}$ , when it gets reflected from the wall. If the speed of sound in air is 345 m/s , then the speed of the car is:

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Contributor-Level 10

f? = frequency heard by wall = f_s (v_s/ (v_s - v_c)
f? = frequency heard by driver after reflection from wall

f? = (v_s + v_c)/v_s)f? = (v_s + v_c)/ (v_s - v_c)f?
f? /f? = (v_s - v_c)/ (v_s + v_c)
48/44 = (v_s - v_c)/ (v_s + v_c)
12 (v_s + v_c) = 11 (v_s - v_c)
23v_c = v_s
v_c = v_s/23 = 345/23 = 15 m/s
= (15 * 18)/5 = 54 km/hr

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2 months ago