JEE Waves PYQs with Video Solutions, Check & Download PDF

A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is:

A wire of length $$L$$ and mass per unit length $$6.0 \times 10^{-3}$$ kg m$$^{-1}$$ is put under tension of 540 N. Two consecutive frequencies that it resonates at are: 420 Hz and 490 Hz. Then $$L$$ in meters is:

A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in m s$$^{-1}$$,
(Given speed of sound = 300 m/s)

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to:

A travelling harmonic wave is represented by the equation $$y(x, t) = 10^{-3} \sin(50t + 2x)$$, where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave?

Displacement of a wave is expressed as $$x(t) = 5\cos\left(628t + \frac{\pi}{2}\right)$$ m. The wavelength of the wave when its velocity is 300 m/s is :

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave train of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wave train (in cm) when it reaches the top of the rope?

For a certain organ pipe, the first three resonance frequencies are in the ratio of $$1 : 3 : 5$$ respectively. If the frequency of fifth harmonic is $$405$$ Hz and the speed of sound in air is $$324$$ m s$$^{-1}$$, the length of the organ pipe is _____ m.

In a Young's double-slit experiment, the slits are separated by a distance of $$0.2\text{ mm}$$ and the screen is placed $$1.2\text{ m}$$ away from the slits. The whole apparatus is immersed in water of refractive index $$4/3$$. If the wavelength of light used in air is $$6000\text{ \AA}$$, the fringe width observed on the screen inside water is:

A uniform rope of mass $$m$$ and length $$L$$ hangs vertically from a rigid support. A transverse wave pulse is produced at the lower free end of the rope. The time taken ($$t$$) by this wave pulse to travel from the bottom to the top support of the rope is given by the expression:

Three harmonic waves having equal frequency $$\nu$$ and same intensity $$I_0$$, have phase angles $$0$$, $$\frac{\pi}{4}$$ and $$-\frac{\pi}{4}$$ respectively. When they are superimposed the intensity of the resultant wave is close to:

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm$$^2$$) is 90 m s$$^{-1}$$. If the Young's modulus of wire is $$16 \times 10^{11}$$ N m$$^{-2}$$, the extension of wire over its natural length is:

A localized wave pulse on a long, taut string with linear mass density $$\lambda$$ is described at any position $$x$$ and time $$t$$ by the wave function:

$$y(x,t) = \frac{b^3}{b^2 + (x - vt)^2}$$

where $$b$$ is a positive constant and $$v$$ represents the propagation velocity of the wave pulse along the string. Determine the total mechanical energy carried by this entire wave pulse.

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $$y = \left(10 \cos \pi x \sin \frac{2\pi t}{T}\right)$$ cm. The amplitude of the particle at $$x = \frac{4}{3}$$ cm will be ______ cm.

Two wires $$W_1$$ and $$W_2$$ have the same radius $$r$$ and respective densities $$\rho_1$$ and $$\rho_2$$, such that $$\rho_2 = 4\rho_1$$. They are joined together at the point $$O$$, as shown in the figure. The combination is used as a sonometer wire and kept under tension $$T$$. The point $$O$$ is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in $$W_1$$ to $$W_2$$ is:

Consider both sources emitting sound. When $$S_2$$ is at R and $$S_1$$ approaches the detector with a speed 4 ms$$^{-1}$$, the beat frequency measured by the detector is ____ Hz.

Two strings (A, B) having linear densities $$\mu_{A}=2\times10^{-4}kg/m\text{ and },\mu_{B}=4\times10^{-4}kg/m$$ and lengths $$L_{A}=2.5m$$ and $$L_{B}=1.5m$$ respectively are joined. Free ends of A and B are tied to two rigid supports C and D, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from C and D ends, take time $$t_{1}\text{ and } t_{2}$$, respectively, to reach the joint. The ratio $$t_{1}/ t_{2}$$ is :

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be ______ %.

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

If a wave gets refracted into a denser medium, then which of the following is true?

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is $$20$$ cm. The length of the open organ pipe is ______ cm

Two cars are approaching each other at an equal speed of 7.2 km hr$$^{-1}$$. When they see each other, both blow horns having a frequency of 676 Hz. The beat frequency heard by each driver will be ______ Hz. [Velocity of sound in air is 340 m s$$^{-1}$$.]

The mass per unit length of a uniform wire is 0.135 g cm$$^{-1}$$. A transverse wave of the form $$y = -0.21\sin(x + 30t)$$ is produced in it, where $$x$$ is in meter and $$t$$ is in second. Then, the expected value of tension in the wire is $$x \times 10^{-2}$$ N. Value of $$x$$ is ______ (Round-off to the nearest integer)

A particle executing simple harmonic motion (SHM) has a maximum velocity $$v_{\text{max}}$$ and a maximum acceleration $$a_{\text{max}}$$. The amplitude ($$A$$) of the motion is given by the expression:

A travelling wave is described by the equation $$y(x, t) = 0.05\sin(8x - 4t)$$ m. The velocity of the wave is: [All the quantities are in SI unit]

In a resonance tube experiment when the tube is filled with water up to a height of $$17.0\,\text{cm}$$, from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of $$24.5\,\text{cm}$$. If the velocity of sound in air is $$330\,\text{m s}^{-1}$$, the tuning fork frequency is:

A person observes two moving trains, $$A$$ reaching the station and $$B$$ leaving the station with equal speed of $$30$$ m s$$^{-1}$$. If both trains emit sounds with frequency $$300$$ Hz, (Speed of sound: $$330$$ m s$$^{-1}$$) approximate difference of frequencies heard by the person will be:

A student is performing the experiment of the resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m s$$^{-1}$$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:

A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be _________ cm. (Take speed of sound in air as 340 m s$$^{-1}$$)

A set of $$20$$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $$4$$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is ______ Hz.