Tag: physics

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Questions Related to physics

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

Find the number of beats produced per sec by the vibrations $x _1=A\sin (320\pi t)$ and $x _2=A\sin (326\pi t)$.

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$X _1=Asin(320\Pi t)$

$X _2=Asin(326\Pi t)$
On comparing it with general equation.
$X=Asin(wt)$
Then, $w _1=320\Pi $
$w _1=2\Pi f$
frequency=160 Hz
Similarly,
$w _2=326\Pi $
$w _2=2\Pi f$
frequency=163 Hz
No of beats=163-160=3

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

In an organ pipe(may be closed or open) of $99$ cm length standing wave is setup, whose equation is given by longitudinal displacement.
$\xi =(0.1mm)\cos \dfrac{2\pi}{0.8}(y+1cm)\cos 2\pi (400)t$
where y is measured from the top of the tube in meters and t is second. Here $1$cm is the end correction.
The air column is vibrating in :

  1. First overtone

  2. Fifth harmonic

  3. Third harmonic

  4. Fundamental mode
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation is of the form cos(k(y+c))cos(wt). The angular frequency w = 2*pi*400, so f = 400 Hz. The wave number k = 2*pi/0.8, so wavelength lambda = 0.8 m = 80 cm. With end correction, the effective length is 99 + 1 = 100 cm. For a closed pipe, L = (2n-1)lambda/4. 100 = (2n-1)80/4 = (2n-1)20. 5 = 2n-1, so n=3. This corresponds to the 5th harmonic.

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

The speed of mechanical waves depends on :-

  1. Density of medium

  2. Elasticity of medium

  3. Elasticity and density of medium

  4. Frequency of the wave.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The speed of a mechanical wave in a medium is determined by the medium's elastic properties (which provide the restoring force) and its inertial properties (density). Both factors are essential for wave propagation.

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

A suspension bridge is to be built across valley where it is known that the wind can gust at $5\ s$ intervals. It is estimated that the speed of transverse waves along the span of the bridge would be $400\ m/s$. The danger of reasonant motions in the bridge at its fundamental frequency would be greater if the span had a length of :

  1. $2000\ m$
  2. $1000\ m$
  3. $400\ m$
  4. $80\ m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Resonance occurs when the driving frequency matches the natural frequency of the system. For a bridge span, the fundamental frequency is f = v / (2L). Given v = 400 m/s and a period of 5s (frequency f = 0.2 Hz), setting 0.2 = 400 / (2L) leads to 0.4L = 400, so L = 1000 m.

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

A man generates a symmetrical pulse in a string by moving his hand up and down . At t = 0 the point in his hand moves downward. the pulse travels with speed of 3 m/s on the string & his hands passes 6 times in each second from the mean position. then the point on the string at a distance 3m will reach its upper extreme first time at times t =

  1. $1.25 sec$
  2. $1 sec$
  3. $\frac{{13}}{{12}}\sec $
  4. $0.25$secs
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The man's hand passes $6$ times from the mean position in $1$ sec, we can find that string creates $3$ cycles after $1$ sec.

Frequency of wave= $3Hz$
$V=f\lambda\Rightarrow \lambda=\cfrac {V}{f}=\cfrac {3}{3}=1m$
To reach upper extreme $\longrightarrow$ have to travel $3\lambda/4$ distance.
Time to travel $\cfrac {3 \lambda}{4}=\cfrac {3}{1}\times \cfrac {1}{3}=\cfrac {1}{4}=0.25$ sec

Multiple choice physics oscillations and waves standing waves in strings standing waves reflection of waves

In a reasonance tube experiment, a closed organ pipe of lenght $120$ cm is used. initially it is completely fiiled with water. It is vibrated with tuning fork of frequency $340$ Hz. To achieve reasonance the water level is lowered then (given ${V _{air}} = 340m/\sec $., neglect end correction):

  1. minimum lenght of water column to have the resonance is 45 cm.

  2. the distance between two successive nodes is 50 cm.

  3. the maximum lenght of water column to resonance is 95 cm.

  4. the distance between two successive nodes is 25 cm.
Reveal answer Fill a bubble to check yourself
D Correct answer