A travelling harmonic wave is given as: y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35).

What is the phase difference between the oscillatory motion of two points separated by a distance of:

**(i)** 8 m,

**(ii)** 1 m,

**(iii)** \(
\dfrac{λ}{2}\),

**(iv)** \(
\dfrac{6λ}{4}\)

[ X and y are in cm and t is in secs ].

Asked by Pragya Singh | 1 year ago | 213

Given,

Equation for a travelling harmonic wave :

y (x, t) = 2.0 cos 2π (10t – 0.0080x + 0.35)

= 2.0 cos (20πt – 0.016πx + 0.70 πWhere,

Propagation constant, k = 0.0160 π

Amplitude, a = 2 cm

Angular frequency, ω= 20 π rad/s

We know,

Phase difference Φ = kx = \(
\dfrac{2π}{λ}\)

**(i)** For x = 8 m = 800 cm

Φ = 0.016 π × 800 = 12.8 π rad

**(ii)** For x = 1 m = 100 cm

Φ = 0.016 π × 100 = 1.6 π rad

**(iii)** For x =\(
\dfrac{λ}{2}\)

Φ = (\(
\dfrac{2π}{λ}\)) x ( \(
\dfrac{λ}{2}\))

= π rad

**(iv)** For x =\(
\dfrac{6λ}{4}\)

Φ = (\(
\dfrac{2π}{λ}\)) x ( \(
\dfrac{6λ}{4}\))

= 3 π rad

A truck parked outside a petrol pump blows a horn of frequency 200 Hz in still air. The Wind then starts blowing towards the petrol pump at 20 m/s. Calculate the wavelength, speed, and frequency of the horn’s sound for a man standing at the petrol pump. Is this situation completely identical to a situation when the observer moves towards the truck at 20 m/s and the air is still?

A man standing at a certain distance from an observer blows a horn of frequency 200 Hz in still air.

**(a)** Find the horn’s frequency for the observer when the man

(i) runs towards him at 20 m/s

(ii) runs away from him at 20 m/s.

**(b)** Find the speed of sound in both the cases. [Speed of sound in still air is 340 m/s]

A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.03 times the speed of sound in the air. What frequency does the bat hear reflected off the wall?

Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of the S wave is about \( 4.0 km s^{–1}\), and that of the P wave is \( 8.0 km s^{–1}.\) A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?

A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of \( 360 km h^{–1}\). What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be \( 1450 m s^{–1}\) .