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The equation ...

Question

The equation for a wave propagating with a velocity of 330 m/s and having a frequency of 110 Hz and amplitude 0.05 m is

y = 0.05 sin 2 π [110 t + \frac{x}{3}]

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y = 0.05 sin 2 π [110 t - \frac{x}{3}]

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y = 0.05 sin 2 π [110 t \pm \frac{x}{3}]

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y = 0.05 sin 2 π [110 t - 330 x]

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Solution

The correct option is C $y = 0.05 sin 2 π [110 t \pm \frac{x}{3}]$
$V = 330 m / s f = 110 H z$ Amplitude $= 0.05 m$
Equation of wave $= A sin (ω t \pm k m) k = \frac{ω}{v} = \frac{2 n f}{v} = \frac{2 π \times 110}{330} = \frac{2 π}{3} ω t = 2 π f t = 2 π \times 110 t$
$∴$ Equation is $0.05 sin (2 π \times 110 t \pm \frac{2 π}{3} x) = 0.05 sin 2 π (110 t \pm \frac{x}{3})$

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Similar questions

Q. For a travelling wave represented by equation,

y = 0.2 sin 2 π (x - 110 t + \frac{1}{2})

(SI units).
The phase difference between particles at

x_{1} = 4.5 m

and

x_{2} = 7 m

Q. For a travelling wave represented by equation,

y = 0.2 sin 2 π (x - 110 t + \frac{1}{2})

(SI units).
The phase difference between particles at

x_{1} = 4.5 m

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x_{2} = 7 m

A source of sound of frequency $50 H z$ is producing longitudinal waves in air. The amplitude of vibrations of air particles is 5mm and the speed of the wave is $330 m s^{- 1}$ . Write the equation of the wave.

Q. the equation of a progressive wave is given by

y = 5

sin

(100 π t - 0.4 π x)

where

y

and

x

are in

m

and

t

is in

s

.
(1) The amplitude of the wave is

5

m

.
(2) The wavelength of the wave is

5

m

.
(3) The frequency of the wave is

50

H z

.
(4) The velocity of the wave is

250

m / s

Which of the following statement are correct?

Q. A wave is represented by the equation

y = (0 \cdot 001 mm) \sin [(50 s^{- 1}) t + (2 \cdot 0 m^{- 1}) x]

.

(a) The wave velocity = 100 m s⁻¹.
(b) The wavelength = 2⋅0 m.
(c) The frequency = 25/π Hz.
(d) The amplitude = 0⋅001 mm.

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The equation for a wave propagating with a velocity of 330 m/s and having a frequency of 110 Hz and amplitude 0.05 m is

The correct option is C y=0.05sin2π[110t±x3]V=330m/sf=110Hz Amplitude =0.05mEquation of wave =Asin(ωt±km)k=ωv=2nfv=2π×110330=2π3ωt=2πft=2π×110t∴ Equation is 0.05sin(2π×110t±2π3x)=0.05sin2π(110t±x3)