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

A string is under tension so that its length is increased by $1/n$ times its original length. The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be

  1. $1:n$
  2. ${n}^{2}:1$
  3. $\sqrt{n}:1$
  4. $n:n+1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The frequency of longitudinal vibrations depends on the speed of sound in the material, while transverse vibrations depend on tension. Calculating the ratio based on the extension 1/n leads to the n/(n+1) relationship.

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

Motion that moves to and fro in regular time intervals is called _________________ motion.

  1. Vibratory

  2. Translatory

  3. Rotatory

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

Sounds are made by vibrations. Some vibrations are easy to see. The vibrations that create sound must travel through a medium, such as air or water, or anything made of molecules. With each forward motion, air molecules pulse outward, pushing other air molecules and crowding them together. With each backward motion, the molecules get less crowded. The forward and backward vibration of the glass creates a chain reaction of crowded and not-so-crowded molecules that ripples through the air. This traveling vibration is called a sound wave. 
Motion that moves to and fro in regular time intervals is called vibratory or oscillatory motion.

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

When we hear a sound, we can identify its source from : 

  1. Amplitude of sound

  2. Intensity of sound

  3. Wavelength of sound

  4. Overtones present in the sound
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Answer is D.

When we hear a sound, we can identify its source from overtones present in the sound.
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials. Together they form the harmonic series.
Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.

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

The length of a stretched string is $2 m$. The tension in it and its mass are $10 N$ and $0.80 kg$ respectively. Arrange the following steps in a sequence to find the third harmonic of transverse wave that can be created in the string.
(a) Find the linear mass density ($m$) using the formula, $m$ $\displaystyle = \dfrac{mass (M)  of \ the \  string}{length (l)  of \ the \  string}$
(b) Collect the data from the problem and find the length($l$) tenstion ($T$) and mass ($M$) of the stretched string.
(c) The fundamental frequency of a stretched vibrating string is given by $n$ $=\displaystyle \dfrac{1}{2l} \sqrt{\dfrac{T}{m}}$
(d) The frequency of $2^{nd}$ overtone or $3^{rd}$ harmonic is given by $n _2\displaystyle = \dfrac{3}{2l}\sqrt{\dfrac{T}{m}}=3n$.

  1. a b c d

  2. d b c a

  3. b a c d

  4. b d c a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Collect the data from the problem and find the length ($l$), tension ($T$) and mass ($M$) of the stretched string (b). 

Find the linear mass density (m) using the formula, m $= m/l$  (a).
The fundamental frequency of a stretched vibrating string is given by, n $=\displaystyle \dfrac{1}{2l} \sqrt{\dfrac{T}{m}}$ (c).
The frequency of $2^{nd}$ overtone or $3^{rd}$ harmonic is given by $n _2=\displaystyle \dfrac{3}{2l} \sqrt{\dfrac{T}{m}}=3n$ (d)

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

A set of 3 standing waves 5, 10 and 15 Hz are to be setup on a string fixed at one end. One of these frequencies are suppressed, while passing through it. Identify them:

  1. 5 Hz

  2. 10 Hz

  3. 15 Hz

  4. All the frequencies will pass through them
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a string fixed at one end, only odd harmonics are allowed and even harmonics are suppressed.

Thus the 10Hz standing wave is suppressed,
The correct option is (b)