Waves

The apparent frequency observed by a moving observer away from a stationary source is 20% less than the actual frequency. If the velocity of sound in air is 330 ms^-1, then the velocity of the observer is

• 660 ms^-1

• 330 ms^-1

• 66 ms^-1

• 33 ms^-1

A string under tension of 129.6 N produces 10 beats/second, when it vibrates along with a tuning fork. When the tension in the string is increased to 160 N, it vibtrates in unison with the tuning fork. Then, frequency of the tuning fork is

• 100 Hz

• 110 Hz

• 90 Hz

• 220 Hz

The ionospheric layer acts as a reflector for the frequency range

• 1 kHz to 10 kHz

• 3 to 30 MHz

• 3 to 30 kHz

• 100 kHz to 1 MHz

Two travelling waves, y₁ = A sin [k(x + ct)] and y₂ = A sin [k(x- ct)] are superposed on a string. The distance between adjacent antinodes is

• $\frac{\mathrm{ct}}{\mathrm{\pi }}$

• $\frac{\mathrm{ct}}{2\mathrm{\pi }}$

• $\frac{\mathrm{\pi }}{\mathrm{k}}$

• $\frac{\mathrm{k}}{\mathrm{\pi }}$

If a stretched wire is vibrating in the second overtone, then the number of nodes and antinodes between the ends of the string are respectively

• 2 and 2

• 1 and 2

• 3 and 4

• 2 and 3

Pick out the correct statement in the following with reference to stationary wave pattern

• In a tube closed at one end, all the harmonics are present

• In a tube open at one end, only even harmonics are present

• The distance between successive nodes is equal to the wavelength

• In a stretched string, the first overtone is the same as the second harmonic

The bulk modulus of a liquid of density 8000 kgm^-3 is 2 x 10⁹ Nm^-2. The speed of sound in that liquid is (in ms^-1)

• 200

• 250

• 500

• 350

The vibrations of a string of length 60 cm fixed at both the ends are represented by the equation $\mathrm{y} = 2 \sin \left(\frac{4\mathrm{\pi x}}{15}\right) \cos \left(96\mathrm{\pi t}\right)$, where x and y are in cm. The maximum number of loops that can be formed in it, is

• 6

• 16

• 5

• 15

The pressure variations in the propagation of sound waves are

• isobaric

• isochoric

• isobaric and isochoric

• adiabatic

A signal of 5 kHz frequency modulates a carrier of frequency 1 MHz and peak voltage 25 V. If the amplitude at the sidebands of the amplitude modulated signal is 5 V, then the modulation index is

• 0.8

• 0.6

• 0.4

• 0.2