JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Waves & Sound

WhatsApp Email

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is ______ degree.

Answer: 120

Solution

Two waves of equal amplitude

A

superpose to give a resultant amplitude

A_{R} = 2 A cos (\frac{Δ ϕ}{2})

. Here the resultant equals a single amplitude,

A_{R} = A

, so

A = 2 A cos (\frac{Δ ϕ}{2})

gives

cos (\frac{Δ ϕ}{2}) = \frac{1}{2}

and

\frac{Δ ϕ}{2} = 6 0^{\circ}

. The phase difference between the two waves is

12 0^{\circ}

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Waves & Sound →

More JEE Main questions on Waves & Sound

Two loudspeakers ( $L_{1}$ and $L_{2}$ ) are placed with a separation of 10 m , as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$ , at equidistance to both loud speakers, is m …
JEE Main 2026View solution →
In an open organ pipe $v_{3}$ and $v_{6}$ are $3^{rd}$ and $6^{th}$ harmonic frequencies, respectively. If $v_{6} - v_{3} = 2200$ Hz then length of the pipe is $____$ mm. (Take velocity of sound in air is $330$ m/s.)
JEE Main 2026View solution →
The velocity of sound in air is doubled when the temperature is raised from $0^{\circ} C$ to $α^{\circ} C$ . The value of $α$ is ______.
JEE Main 2026View solution →
The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x is ____.
JEE Main 2026View solution →
A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will
JEE Main 2026View solution →
The speed of a longitudinal wave in a metallic bar is $400 m / s$ . If the density and Young's modulus of the bar material are increased by $0.5%$ and $1%$ respectively then the speed of the wave is changed approximately to ______ …
JEE Main 2026View solution →