The following two waves are sent in opposite directions on a horizontal string to create a standing wave in a vertical plane: y 1 ( x , t ) = ( 6 . 00 mm ) sin ( 12 . 0 π x - 300 π t ) y 2 ( x , t ) = ( 6 . 00 mm ) sin ( 12 . 0 π x + 300 π t ) with x in meters and t in seconds. An antinode is located at point A . In the time interval that point takes to move from maximum upward displacement to maximum downward displacement, how far does each wave move along the string?

Given that, two waves are traveling in opposite direction along a string as given below, y 1 = 6 mm sin ⁡ 12 π x - 300 π t y 2 = 6 mm sin ⁡ 12 π x + 300 π t Here x is in meter and t is in seconds. Both waves are having same amplitude and frequency. Resultant wave equation of superposed waves y 1 and y 2 is, y = y 1 + y 2 = 6 mm sin ⁡ 12 π x - 300 π t + 6 mm sin ⁡ 12 π x + 300 π t y = 2 6 mm sin ⁡ 12 π x cos ⁡ 300 π t y = 12 mm sin ⁡ 12 π x cos ⁡ 300 π t . . . 1 The above equation looks like, y = 2 A sin ⁡ k x cos ⁡ ω t . . . 2 By comparing equation 1 & 2 we get, Angular wave numbers, k = 12 π m - 1 Angular frequency, ω = 300 π s - 1 . Speed of the wave is, v = ω k v = 300 π 12 π ⇒ v = 25 m s - 1 The time taken to move from maximum upward displacement to maximum downward displacement is t = T 2 = 1 2 2 π ω ⇒ t = π ω t = π 300 π ⇒ t = 1 300 s = 0 .0033 s Distance covered by each wave along the string is, x = v t ⇒ x = 25 1 300 x = 1 12 m = 0 .083 m We can write directly the distance between two adjacent anti nodes is, x = λ 2 = 1 2 2 π k ⇒ x = 1 2 2 π 12 π x = 1 12 m ≅ 0 .083 m

MEDIUM

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IMPORTANT

Earn 100

What are

(a) the lowest frequency

(b) the second lowest frequency

(c) the third lowest frequency

for standing waves on a wire that is $10.0 m$ long, has a mass of $100 g$ , and is stretched under a tension of $275 N$ ?

Important Questions on Waves-I

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IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 46

A sand scorpion can detect the motion of a nearby beetle (its prey) by the waves the motion sends along the sand surface (in the figure shown below). The waves are of two types, transverse waves travelling at $v_{t} = 50 m s^{- 1}$ and longitudinal waves traveling at $v_{l} = 150 m s^{- 1}$ . If a sudden motion sends out such waves, a scorpion can tell the distance of the beetle from the difference $∆ t$ in the arrival times of the waves at its leg nearest the beetle. What is the time difference if the distance to the beetle is $37.5 cm ?$

Question Image

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JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 47

Two sinusoidal waves of the same period, with amplitudes of

5.0

and

7.0 mm

, travel in the same direction along a stretched string. They produce a resultant wave with an amplitude of

10.0 mm

. The phase constant of the

5.0 mm

wave is

0

. What is the phase constant of the

7.0 mm

wave?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 48

A sinusoidal wave is travelling on a string with speed $40 cm s^{- 1}$ . The displacement of the particles of the string at $x = 10 cm$ varies with time according to $y = (4.0 cm) s i n [5.0 - (4.0 s^{- 1}) t] .$ The linear density of the string is $4.0 g {cm}^{- 1} .$ What are
(a) the frequency
(b) the wavelength of the wave?

If the wave equation is of the form $y (x, t) = y_{m} s i n (k x \pm ω t),$ what are
(c) $y_{m}, (d) k, (e) ω,$
(f) the correct choice of sign in front of $ω$
(g) What is the tension in the string?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 49

The following two waves are sent in opposite directions on a horizontal string to create a standing wave in a vertical plane:

\begin{array}{l} y_{1} (x, t) = (6.00 mm) \sin (12.0 π x - 300 π t) \\ y_{2} (x, t) = (6.00 mm) \sin (12.0 π x + 300 π t) \end{array}

with

x

in meters and

t

in seconds. An antinode is located at point

A

. In the time interval that point takes to move from maximum upward displacement to maximum downward displacement, how far does each wave move along the string?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 50

Four waves are to be sent along the same string, in the same direction:

\begin{array}{l} y_{1} (x, t) = (5.00 mm) \sin (4 π x - 400 π t) \\ y_{2} (x, t) = (5.00 mm) \sin (4 π x - 400 π t + 0.8 π) \\ y_{3} (x, t) = (5.00 mm) \sin (4 π x - 400 π t + π) \\ y_{4} (x, t) = (5.00 mm) \sin (4 π x - 400 π t + 1.8 π) \end{array}

What is the amplitude of the resultant wave?

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JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 51

If a wave

y (x, t) = (5.0 mm) \sin (k x + (600 rad s^{- 1}) t + ϕ)

travels along a string, how much time does any given point on the string take to move between displacements

y = + 2.0 mm

and

y = - 2.0 mm ?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 52

A string along which waves can travel is

2.70 m

long and has a mass of

130 g

. The tension in the string is

36.0 N

. What must be the frequency of traveling waves of amplitude

7.70 mm

for the average power to be

170 W ?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 53

A uniform rope of mass

m

and length

L

hangs from a ceiling.
(a) Show that the speed of a transverse wave on the rope is a function of

y

, the distance from the lower end, and is given by

v = \sqrt{g y}

(b) Show that the time a transverse wave takes to travel the length of the rope is given by

t = 2 \sqrt{\frac{L}{g}}

What are (a) the lowest frequency (b) the second lowest frequency (c) the third lowest frequency for standing waves on a wire that is 10.0 m long, has a mass of 100 g, and is stretched under a tension of 275 N ?

Important Questions on Waves-I

Learn and Prepare for any exam you want !

What are

(a) the lowest frequency

(b) the second lowest frequency

(c) the third lowest frequency

for standing waves on a wire that is $10.0 m$ long, has a mass of $100 g$ , and is stretched under a tension of $275 N$ ?