An ambulance siren has frequency 250 Hz. The ambulance is headed towards an
accident site with a speed of 90 km h−1, Two police officers on separate motor
cycles head for the same accident site: one follows the ambulance with a speed of
80 km h−1 and the other approaches the accident site from the other direction with a
speed of 80 km h−1. What frequency does ambulance siren has for each of the police
officers? Take the speed of sound equal to 340 ms−1.
We use the equation for the Doppler Effect:
here c is the velocity of waves in the medium;vr is the velocity of the receiver relative to themedium; positive if the receiver is moving towards the source (and negative in the other direction); v s is the velocity of
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An ambulance siren has frequency 250 Hz. The ambulance is headed towards an
accident site with a speed of 90 km h−1, Two police officers on separate motor
cycles head for the same accident site: one follows the ambulance with a speed of
80 km h−1 and the other approaches the accident site from the other direction with a
speed of 80 km h−1. What frequency does ambulance siren has for each of the police
officers? Take the speed of sound equal to 340 ms−1.
What is the effect of damping in an oscillatory system? Differentiate between heavy and critical damping. Show that the displacement of a weakly damped oscillator is given by
x(t ) = a0 exp(−bt ) cos(ωd t − φ)
where symbols have their usual meanings.
A harmonic wave on a rope is described by
i) Calculate the wavelength and time period of the wave. ii) Determine the
displacement and acceleration of the element of the rope located at x = 0.58 m at
time, t = 0.41 s.
A sinusoidal wave is described by
y(x, t) = 3.0 sin (5.95t − 4.20x) cm
where x is the position along the wave propagation. Determine the amplitude, wave
number, wavelength, frequency and velocity of the wave.
Giving the necessary mathematical expressions, discuss the transient and steady state of a weakly damped forced oscillator. Show that the average power absorbed by a forced oscillator is given by
A body of mass 0.15 kg executes SHM described by the equation
x(t ) = 2 sin(πt + π / 4)
where x is in meters and t is in seconds.
i) Determine the amplitude and time period of the oscillation.
ii) Calculate the initial values of displacement and velocity.
iii) Calculate the values of time when the energy of the oscillator is purely kinetic.
The amplitude of an oscillator is 8 cm and it completes 100 oscillations in 80s.
i) Calculate its time period and angular frequency. ii) If the initial phase is π/4, write expressions for its displacement and velocity. iii) Calculate the values of maximum
velocity and acceleration