Tag: wave velocity

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Questions Related to wave velocity

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A transverse wave on a string has an amplitude of $02m$ and a frequency of $175Hz$. Consider a particle of the string at $x=0$. It begins with a displacement $y=0$ at $t=0$, according to equation $y=0.2\sin{(kx+\omega t)}$. How much time passes between the first two instant when this particle has a displacement of $y=0.1m$>

  1. $1.9ms$
  2. $3.9ms$
  3. $2.4ms$
  4. $0.5ms$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

For a string clamped at both its ends, which of the following wave equation is/are valid for a stationary wave set up in it? (Origin is at one end of string).

  1. $y=A\sin kx.\sin \omega t$
  2. $y=A\cos kx \sin \omega t$
  3. $y=A\sin kx. \cos \omega t$
  4. $y=A\cos kx \cos \omega t$
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

For all values of t, y$=0$ at $x=0$
Hence, (A) and (C) are correct.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A certain strings will resonate to several frequencies , the lowest of which is $200$cps.what are the next three higher frequencies to which it resonates? 

  1. $400,600,800$
  2. $300,400,500$
  3. $100,150,200$
  4. $200,250,300$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given,  The Lowest frequency is $200cps$

Let  $f$ resonant the fundamental frequency, then the next higher frequency is: $2f,3f,4f$

$2\times200=400cps,3\times200=600,4\times200=800cps$


Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The string of a violin emits a note of 205 Hz at its correct tension. The string is tightened slightly and then it produces six beats in two seconds with a tuning fork of frequency 205 Hz. The frequency of the note emitted by the taut string is

  1. 211 HZ

  2. 199 Hz

  3. 208 Hz

  4. 202 Hz
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The initial frequency is 205 Hz. When tightened, the string produces 6 beats in 2 seconds, meaning the beat frequency is 6 / 2 = 3 Hz. Tightening a string increases its tension and thus its frequency. Therefore, the new frequency must be 205 + 3 = 208 Hz.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 Hz$. The mass of the wire is $3.5 \times 10^{-2}kg$ and its linear mass density is $4.0 \times 10^{-2} kgm^{-1}$. What is the speed of a transverse wave on the wire?

  1. $69 \ ms^{-1}$
  2. $79 \ ms^{-1}$
  3. $89 \ ms^{-1}$
  4. $99 \ ms^{-1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a wire vibrating in its fundamental mode, the frequency f = v / (2L). However, we can use the relation v = sqrt(T/mu). Given the mass M = 0.035 kg and linear density mu = 0.04 kg/m, the length L = M/mu = 0.875 m. The fundamental frequency f = v / (2L) = 45 Hz, so v = 45 * 2 * 0.875 = 78.75 m/s, which rounds to 79 m/s.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A person observe two points on a string as a travelling wave passes them. The points are at $x _ { 1 } = 0$ and $x _2 = 1m$. The transverse motions of the two points are found to be as follows: $y _ { 1 } = 0.2 \sin 3 \pi t$
$y _ { 2 } = 0.2 \sin ( 3 \pi t + \pi/8 )$ What is the frequency in Hertz?

  1. $1.5 Hz$
  2. $3 Hz$
  3. $4.5 Hz$
  4. $1 Hz$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The transverse motion is given by y = A sin(omega * t + phi). Comparing y1 = 0.2 sin(3 * pi * t) with the standard form, omega = 3 * pi. Since omega = 2 * pi * f, we have 3 * pi = 2 * pi * f, which gives f = 1.5 Hz.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

If $n,2n,3n$ are the fundamental frequencies of the three segments into which a string is divided by placing required number of bridges below it. If $n _0$ is the fundamental frequency of the string, then 

  1. $n _0=3n$
  2. $n _0=6n$
  3. $n _0=\dfrac{3n}{5}$
  4. $n _0=\dfrac{6n}{11}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The fundamental frequency of a string is f = v / (2L). When divided into segments of lengths L1, L2, L3, the frequencies are f1 = v / (2L1) = n, f2 = v / (2L2) = 2n, f3 = v / (2L3) = 3n. The total length L = L1 + L2 + L3 = v/(2n) + v/(4n) + v/(6n) = (6+3+2)v / 12n = 11v / 12n. The fundamental frequency of the whole string is f0 = v / (2L) = v / (2 * 11v / 12n) = 6n / 11.

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A spring of force constant K is first stretched by distance a from its natural length and then future by distance b. The work done in stretching the part b is

  1. $\dfrac{1}{2}$Ka(a-b)
  2. $\dfrac{1}{2}$Ka(a+b)
  3. $\dfrac{1}{2}$Kb(a-b)
  4. $\dfrac{1}{2}$Kb(2a+b)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work done by spring in its natural length$=\cfrac{1}{2} \times k \times x^{2}= \cfrac{1}{2} \times k \times a^{2}$

So, total work$=\cfrac{1}{2}k(a+b)^{2}$
for work done for stretching 'b'
$\cfrac { 1 }{ 2 } \times k\times (a+b)^{ 2 }-\cfrac { 1 }{ 2 } \times k\times a^{ 2 }=\cfrac { 1 }{ 2 } \times k\times b\times (2a+b)$