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A steel wire fixed at both ends has a fundamental frequency of 200 Hz. A person can hear sound of maximum frequency 14 kHz. What is the highest harmonic that can be played on this string which is audible to the person?

Fundamental frequency = fo =200 Hznth harmonic = f' = n × fundamental frequencyand frequency of the highest harmonic = 14 kHz = 14000 HzNow,... View Article

A particular guitar wire is 30.0 cm long and vibrates at a frequency of 196 Hz when no finger is placed on it. The next higher notes on the scale are 220 Hz, 247 Hz, 262 Hz and 294 Hz. How far from the end of the string must the finger be placed to play these notes?

We know that, f ∝ 1/l or f = v/l (where v = constant for a medium)l1 = 30 cm or 0.3 m (given)f1 = 196 Hz and f2 = 220 Hz (given)Now, f1/f2 =... View Article

A 660 Hz tuning fork sets up vibration in a string clamped at both ends. The wave speed for a transverse wave on this string is 220 m s⁻¹ and the string vibrates in three loops.

Solution : f = 660 Hz and v = 220 m/sWave length = λ = v/f = 1/3 m Number of loops = n =3Therefore, L = (nλ)/2 = (3/2) x (1/3) = 1/2 m = 50 cm... View Article

A string, fixed at both ends, vibrates in a resonant mode with a separation of 2.0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1.6 cm. Find the length of the string.

Let n be the frequency, L is length of the string and λ be the distance between two consecutive nodes.Therefore, L = nλfor next higher frequency,... View Article

A wire, fixed at both ends is seen to vibrate at a resonant frequency of 240 Hz and also at 320 Hz.

(a) What could be the maximum value of the fundamental frequency? (b) If transverse waves can travel on this string at a speed of 40 m s−1, what... View Article

A one-metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops?

Using relation, L = nλ/2Here n = 4 and L = 1 m=> λ = 0.5Also, v = fλ = √(T/m)=> T = f2λ2 m = 1282 x 0.52 x 40 x 10-3= 164 N... View Article

The length of the wire shown in figure (below) between the pulley is 1.5 m and its mass is 12.0 g. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest.

Solution:Mass of the wire = 12 gmLength of the wire between two pulleys (L) = 1.5 mso, Mass per unit length = m = (12/1.5) g/m = 8 x 10-3... View Article

A sonometer wire having a length of 1.50 m between the bridges vibrates in its second harmonic in resonance with a tuning fork of frequency 256 Hz. What is the speed of the transverse wave on the wire?

Fundamental frequency of First Harmonic = 256/2 = 128 HzHere, Second harmonic= 2 × First HarmonicWhen the fundamental wave is produced, λ/2 =... View Article

A piano wire weighing 6.0 g and having a length of 90.0 cm emits a fundamental frequency corresponding to the “Middle C” (ν = 261.63 Hz). Find the tension in the wire.

Fundamental frequency = f = (1/2L)√(T/m)or f = √150 TAlso, f = 261.63 Hz (given)=> 261.63 = √150 T=> T = 1480 N (approx.)... View Article

A steel wire of mass 40 g and length 80 cm is fixed at the two ends. The tension in the wire is 50 N. Find the frequency and wavelength of the fourth harmonic of the fundamental.

Fundamental frequency = f = v/2L = 1/2L x √(T/m) = 62.5 Hz frequency of 4th harmonic = F4 = 4 x 62.5 = 250 Hz Now, v4 = F4 λ4 or λ4 =... View Article

A wire of length 200 m is stretched to a tension of 160 N. If the fundamental frequency of vibration is 100 Hz, find its linear mass density.

Fundamental frequency = f = v/2L = 1/2L x √(T/m) = 1 g/m... View Article

If the speed of a transverse wave on a stretched string of length 1 m is 60 m s−1, what is the fundamental frequency of vibration?

Fundamental frequency = f = v/2L = 30 Hz... View Article

Two waves, each having a frequency of 100 Hz and a wavelength of 2.0 cm, are travelling in the same direction on a string. What is the phase difference between the waves

(a) if the second wave was produced 0.015 s later than the first one at the same place, (b) if the two waves were produced at the same instant... View Article

Figure shows two wave pulses at t = 0 travelling on a string in opposite directions with the same wave

Solution:Distance travelled by any classical wave = s = vtAt t = 4 => s = 4 x 10-3 x 50 x 10 = 2 mmAt t = 6 => s = 6 x 10-3 x 50 x 10 = 3... View Article

Two waves, travelling in the same direction through the same region, have equal frequencies, wavelengths and amplitudes. If the amplitudes of each wave is 4 mm and the phase difference between the waves is 90°, what is the resultant amplitude?

y' = r sin ωt and y'' = r sin (ωt + π/2)Now, y = y' + y''Or y = √2 r sin(ωt + π/4)The amplitude is 4√2 mm... View Article