Wave properties Quiz 1

Question 1

In order to demonstrate the visualization of standing waves, Prof. B brings a small slinky to his class and asks one of his students to volunteer and hold one end of the slinky and stretch it out to the maximum while he holds the other end and strikes it to make it oscillate. If the slinky bobs up and down 10 times in 5 seconds when his student is standing $$6 m$$ from him, what would be the frequency of the standing wave? Determine its wavelength and speed if the standing wave consists of four antinodes.

Accepted Answer

$$2 Hz$$, $$3 m$$, $$6 ms^{-1}$$

Answer

$$50 Hz$$, $$2 m$$, $$6 ms^{-1}$$

Answer

$$2 Hz$$, $$1.5 m$$, $$3 ms^{-1}$$

Answer

$$20 Hz$$, $$1.5 m$$, $$3 ms^{-1}$$

Question 2

Imagine that you are hiking down a road and you see an old car coming your way. It’s one of those late 90’s cars that has an antenna, which is basically an extendable metal rod that is used to pick up low static radio signals for the purpose of music and entertainment. You observe an odd vibrational pattern on the antenna as shown in the figure, with a node at its fixed end and an antinode at its free end. If these vibrations propagate through the $$75 cm$$ long antenna at the rate of $$5 ms^{-1}$$, determine its frequency.  $$ \ $$<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/41a1f1ac-f712-4830-b1a0-c245a7cb04d38727020818536951189.png"/>

Accepted Answer

$$5 Hz$$

Answer

$$4 Hz$$

Answer

$$0.04 Hz$$

Answer

$$0.5 Hz$$

Question 3

You decide to spend an exquisite evening at the Sydney Opera House on your trip to Australia and watch the Phantom of The Opera. The theme song of this theatrical play is known for its initial notes played on the pipe organ that embosses the overbearing tone of the scene onto the audience. If two open pipe organs when played together produce this note at the rate of three beats per second, find their frequency if one of the pipes is $$30 cm$$ long and the other is $$30.3 cm$$ long respectively.

Accepted Answer

$$151.5 Hz$$ and $$150 Hz$$

Answer

$$50 Hz$$ and $$100 Hz$$

Answer

$$303.2 Hz$$ and $$273.2 Hz$$

Answer

$$15.2 Hz$$ and $$15 Hz$$

Question 4

Suppose that you and your friend are kayaking in the shallow backwaters of Kerala and your kayaks are spaced at $$2 m$$ from each other when a motorboat zooms past at a distance, creating ripples that are propagating towards your kayaks. Your kayaks begin to bob up and down about $$ 5$$ times in a span of $$10 s$$ as the ripples pass. When your kayak was at a high point, your friend’s kayak was at a low point and vice versa with no crests between the two of you. Assuming that the ripples travelled in a direction parallel to the imaginary line connecting the two kayaks, determine the wavelength, frequency and speed with which the ripples travelled.

Accepted Answer

$$4 m$$, $$0.5 Hz$$, $$2 ms^{-1}$$

Answer

$$2 m$$, $$0.5 Hz$$, $$1 ms^{-1}$$

Answer

$$2 m$$, $$1 Hz$$, $$2 ms^{-1}$$

Answer

$$4 m$$, $$2 Hz$$, $$8 ms^{-1}$$

Question 5

For the propagation of waves through a string, the tension of the string is essential for producing a disturbance in the string and the mass of the string is what drives the disturbance by lending it suitable kinetic energy. Suppose you have a stretched string of linear mass density $$ \mu$$ possessing a tension T along its length, determine the speed of transverse waves that can be set up in this stretched string. Should you require the need for a constant of proportionality in your evaluation, set it to 1 as we do experimentally.

Accepted Answer

$$\sqrt{\dfrac{T}{\mu}}$$

Answer

$$\sqrt{\dfrac{\mu}{T}}$$

Answer

$$\dfrac{T}{\mu}$$

Answer

$$\dfrac{\mu}{T}$$