A soap bubble is essentially a very thin film of water 1n = 1.332 surrounded by air. The colors that you see in soap bubbles are produced by interference.
a. Derive an expression for the wavelengths lC for which constructive interference causes a strong reflection from a soap bubble of thickness d. Hint: Think about the reflection phase shifts at both boundaries.
b. What visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble? What color would such a soap bubble appear to be?
a) The constructive interference is
b) The visible wavelength is 691. 6 nm dark red and 414 .96 nm dark blue.
The distance line between the waves is known as the wavelength.
The wavelength of the light is traveling with speed thus
Thus, the formula of the wavelength is
Thus, the spectrum is (400-800)nm thus the calculation of the value n is
the extremum will be
The other one will be
The integer values of n are 1 and 2. The interferences of the integers are 691.6nm and 414. 96 nm.
Traditional Indonesian music uses an ensemble called a gamelan that is based on tuned percussion instruments somewhat like gongs. In Bali, the gongs are often grouped in pairs that are slightly out of tune with each other. When both are played at once, the beat frequency lends a distinctive vibrating quality to the music. Suppose a pair of gongs are tuned to produce notes at 151 Hz and 155 Hz. How many beats are heard if the gongs are struck together and both ring for 2.5 s?
Piano tuners tune pianos by listening to the beats between the
harmonics of two different strings. When properly tuned, the note
A should have a frequency of 440 Hz and the note E should be
at 659 Hz.
a. What is the frequency difference between the third harmonic
of the A and the second harmonic of the E?
b. A tuner first tunes the A string very precisely by matching it to
a 440 Hz tuning fork. She then strikes the A and E strings simultaneously
and listens for beats between the harmonics. What
beat frequency indicates that the E string is properly tuned?
c. The tuner starts with the tension in the E string a little low,
then tightens it. What is the frequency of the E string when
she hears four beats per second?
FIGURE EX17.28 shows the circular wave fronts emitted by two
a. Are these sources in phase or out of phase? Explain.
b. Make a table with rows labeled P, Q, and R and columns
labeled and C/D. Fill in the table for points P, Q,
and R, giving the distances as multiples of l and indicating,
with a C or a D, whether the interference at that point is
constructive or destructive.
A 25-cm-long wire with a linear density of 20 g/m passes across the open end of an 85-cm-long open-closed tube of air. If the wire, which is fixed at both ends, vibrates at its fundamental frequency, the sound wave it generates excites the second vibrational mode of the tube of air. What is the tension in the wire? Assume vsound = 340 m/s.
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