Physics Waves

An observer moves towards a stationary source of sound with a velocity one-fourth of the velocity of sound. What is the percentage increase in the apparent frequency?

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Contributor-Level 10

$f' = f ⌊ \frac{v + \frac{v}{4}}{v} ⌋ = \frac{5 f}{4}$

$\Rightarrow \frac{f'}{f} = \frac{5}{4}$

$\Rightarrow \frac{Δ f}{f} = \frac{1}{4}$

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Equation of a standing wave is expressed as y = 2Asinωtcoskx. In this equation, quantity ω/k represents

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Contributor-Level 10

Equation of component waves are

y = Asin (ωt – kx) and y = Asin (ωt + kx)

So speed of component wave is ω/k

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A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

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Contributor-Level 10

Frequency increases on filing. So, initial frequency of A is 335 Hz.

f = 340 – 5 = 335 Hz

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The velocity of sound in a gas, in which two wavelengths 4.08m and 4.16m produce 40 beats in 12s, will be:

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Raj Pandey

Contributor-Level 9

$| f_{1} - f_{2} | = \frac{40}{12} = \frac{10}{3}$

$\Rightarrow v (\frac{1}{λ_{1}} - \frac{1}{λ_{2}}) = \frac{10}{3}$

$\Rightarrow V = \frac{10}{3} * \frac{λ_{1} λ_{2}}{λ_{2} - λ_{1}} = \frac{10}{3} * \frac{4.08 * 4.16}{. 08} = \frac{10}{3} * \frac{408 * 4.16}{8} = 707.2 m / s$

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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

Answer (3)

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

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A wave given by equation y = 1mm sin $(\frac{n x}{30} - 5 n t)$ is produced in a string 100m long of mass 1 kg. What is the tension (in N) in string? x is in m & t in sec.

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Contributor-Level 10

$v = \frac{ω}{k} = \frac{5 π * 30}{π} = 150 = \sqrt[]{\frac{\frac{T}{1}}{100}}$

$\Rightarrow T = \frac{2250000}{100} = 225 N$

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Speed of sound in a resonance tube experiment is given by the expression v = 2f₀(l₂ – l₁) where f? is the frequency of the tuning fork and l₁, l₂ are length of the air column. Consider f₀ = 300 Hz with no error in its value. Lengths of the air column l₁ and l₂ are measured as 25.0 cm and 80.0 cm respectively. Find the absolute error in the speed of sound (in m/s).

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Contributor-Level 10

Δν = 2f? (Δl? + Δl? ) = 2 * 300 (0.1 + 0.1) * 10? ² = 1.2 m/s

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a month ago

As a train moving with constant speed crosses the platform, the apparent frequency heard by a person standing on the platform during approach and recession differ by 2% of the actual frequency of the horn. If the speed of sound is 330 m/s, find the approximate speed of the train.

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Contributor-Level 10

f? = f? (330/ (330-V) f? = f? (330/ (330+V)
(f? - f? )/f? * 100 = 2% ⇒ (330/ (330-V) - (330/ (330+V) = 0.02
⇒ 330 [ (2V)/ (330)²-V²)] = 0.02 ⇒ 330V = 0.01 * (330)² ⇒ V = 3.3 m/s (approx.)

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The absolute temperature of air in a region linearly increases from $T_{1}$ to $T_{2}$ in a space of width d. The time taken by the sound wave to travel in this region is (The velocity of sound at 273 k is v ):

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Raj Pandey

Contributor-Level 9

$V = \sqrt[]{\frac{γ R T}{M}},$ where, $T = T_{1} + \frac{T_{2} - T_{1}}{d} x$ $_{} \frac{_{}_{}}{}$

Also, $v = \sqrt[]{\frac{γ R 273}{M}} \Rightarrow \sqrt[]{\frac{γ R}{M}} = \frac{v}{\sqrt[]{273}}$ $\frac{}{} \frac{}{} \frac{}{}$

Also, $V = \frac{d x}{d t} = \sqrt[]{\frac{γ R T}{M}}$ $\Rightarrow \int_{0}^{d} ? \frac{d x}{\sqrt[]{T_{1} + \frac{T_{2} - T_{1}}{d} x}} = \sqrt[]{\frac{γ R}{M}} \int_{0}^{t} ? d t$ $\frac{}{} \frac{}{}$

$\Rightarrow t = \frac{\sqrt[]{273}}{v} \cdot \frac{2 d}{T_{2} - T_{1}} (\sqrt[]{T_{2}} - \sqrt[]{T_{1}}) ∴ t = \frac{2 d}{v} \frac{\sqrt[]{273}}{\sqrt[]{T_{1}} + \sqrt[]{T_{2}}}$

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A sound source is located somewhere along the x-axis. Experiment shows that the same wavefront simultaneously reaches listeners at x = -10m and x = +4.0m. A third listener is positioned along the positive y-axis. What is y-coordinate (in m) if the same wavefront reaches at him at the same instant it does the first two listeners?

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