Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by fn+1 = r fn for all n. In this system, the frequency doubles every 12notes—an interval called an octave.
a. What is the value of r?
b. Orchestras tune to the note A, which has a frequency of440 Hz. What is the frequency of the next note of the scale (called A-sharp)?
a) The value of the r is 1.0595
b) The frequency of the next scale note is 466 Hz
The higher and the lower frequencies waves are responsible for oscillating the higher and lower notes.
The provided information is
the separation of the two notes are
Thus, the separation of the 12th notes are
The double of the twelve-note is
based on the simplifaction the remaining value is
Now the r is =
Thus, the determination of the r based on the formula is
Ultrasound has many medical applications, one of which is to monitor fetal heartbeats by reflecting ultrasound off a fetus in the womb.
a. Consider an object moving at speed toward an at-rest source that is emitting sound waves of frequency . Show that the reflected wave (i.e., the echo) that returns to the source has a Doppler-shifted frequency
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?
In a laboratory experiment, one end of a horizontal string is tied
to a support while the other end passes over a frictionless pulley
and is tied to a 1.5 kg sphere. Students determine the frequencies
of standing waves on the horizontal segment of the string, then
they raise a beaker of water until the hanging 1.5 kg sphere is
completely submerged. The frequency of the fifth harmonic with
the sphere submerged exactly matches the frequency of the third
harmonic before the sphere was submerged. What is the diameter
of the sphere?
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