HARD

JEE Main

IMPORTANT

Earn 100

Two sinusoidal waves with the same amplitude and wavelength travel through each other along a string that is stretched along the $x$ axis. Their resultant wave is shown twice in the figure shown below, as the antinode $A$ travels from an extreme upward displacement to an extreme downward displacement in $6.0 ms$ . The tick marks along the axis are separated by $15 cm$ , height $H$ is $1.20 cm .$ Let the equation for one of the two waves be of the form $y (x, t) = y_{m} \sin (k x + ω t) .$ In the equation for the other wave, what are

(a) $y_{m}$

(b) $k$

(c) $ω$

$(d)$ the sign in front of $ω ?$

Important Questions on Waves-I

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 1

A stretched string has a mass per unit length of

5.00 g {cm}^{- 1}

and a tension of

10.0 N

. A sinusoidal wave on this string has an amplitude of

0.16 mm

and a frequency of

100 Hz

and is travelling in the negative direction of an

x

-axis. If the wave equation is of the form

y (x, t) = y_{m} \sin (k x \pm ω t)

, what are
(a)

y_{m}

(b)

k

(c)

ω

and (d) the correct choice of sign in front of

ω

EASY

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 2

The heaviest and lightest strings on a certain violin have linear densities of

3.2 g m^{- 1}

and

0.26 g m^{- 1}

. What is the ratio of the diameter of the heaviest string to that of the lightest string, assuming that the strings are of the same material?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 3

A string fixed at both ends is

7.50 m

long and has a mass of

0.120 kg .

It is subjected to a tension of

96.0 N

and is set oscillating.
(a) What is the speed of the waves on the string?
(b) What is the longest possible wavelength for a standing wave?
(c) Give the frequency of that wave.

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 4

The equation of a transverse wave on a string is

y = (2.0 mm) \sin [(15 m^{- 1}) x - (900 rad s^{- 1}) t]

.
The linear density is

4.17 g m^{- 1}

(a) What is the wave speed? What is the tension in the string?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 5

Two waves are generated on a string of length

4.0 m

to produce a three-loop standing wave with an amplitude of

1.0 cm

. The wave speed is

100 m s^{- 1}

. Let the equation for one of the waves be of the form

y (x, t) = y_{m} \sin (kx + ωt) .

In the equation for the other wave, what are
(a)

y_{m}

(b)

k

and

ω

(d)

the sing in front of

ω

MEDIUM

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 6

What phase difference between two identical traveling waves moving in the same direction along a stretched string that results in the combined wave having an amplitude

0.852

times that of the common amplitude of the two combining waves? Express your answer in (a) degrees, (b) radians and (c) wavelengths.

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 7

100 g

wire is held under a tension of

220 N

with one end at

x = 0

and the other at

x = 10.0 m

. At time

t = 0,

pulse

1

is sent along the wire from the end at

x = 10.0 m

. At time

t = 30.0 ms

pulse

2

is sent along the wire from the end at

x = 0 .

At what position

x

do the pulses begin to meet?

HARD

JEE Main

IMPORTANT

Principles Of Physics International Student Version>Chapter 16 - Waves-I>Problems>Q 8

String

A

is stretched between two clamps separated by distance

L

. String

B

with the same linear density and under the same tension as string

A

is stretched between two clamps separated by distance

3 L

. Consider the first eight harmonics of string

B

. For which of these eight harmonics of

B

(if any) does the frequency match the frequency of (a)

A

's first harmonic, (b)

A

's second harmonic and (c)

A

's third harmonic?

Important Questions on Waves-I

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