FIGURE Q17.1 shows a standing wave oscillating on a string at frequency $f_0$.

1. What mode (m-value) is this?

2. How many antinodes will there be if the frequency is doubled to $2f_0?$

FIGURE Q17.1

If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat. What has happened to the energy of the wave at those instants?

FIGURE Q17.3 shows the displacement of a standing sound wave in a 32-cm-long horizontal tube of air open at both ends.

1. What mode (m-value) is this?

2. Are the air molecules moving horizontally or vertically? Explain.

3. At what distances from the left end of the tube do the molecules oscillate with maximum amplitude?

4. At what distances from the left end of the tube does the air pressure oscillate with maximum amplitude?

FIGURE Q17.3

An organ pipe is tuned to exactly 384 Hz when the room temperature is $20\text{°}$C. If the room temperature later increases to $22\text{°}$C, does the pipe’s frequency increase, decrease, or stay the same? Explain.

If you pour liquid into a tall, narrow glass, you may hear sound with a steadily rising pitch. What is the source of the sound? And why does the pitch rise as the glass fills?

A flute filled with helium will, until the helium escapes, play notes at a much higher pitch than normal. Why?

In music, two notes are said to be an octave apart when one note is exactly twice the frequency of the other. Suppose you have a guitar string playing frequency $f_0$. To increase the frequency by an octave, to $2f_0$, by what factor would you have to (a) increase the tension or (b) decrease the length?

FIGURE Q17.8 is a snapshot graph of two plane waves passing through a region of space. Each wave has a 2.0 mm amplitude and the same wavelength. What is the net displacement of the medium at points 1, 2, and 3?

FIGURE Q17.8

FIGURE Q17.9 shows the circular waves emitted by two in-phase sources. Are 1, 2, and 3 points of maximum constructive interference, maximum destructive interference, or in between?

FIGURE Q17.9

A trumpet player hears 5 beats per second when she plays a note and simultaneously sounds a 440 Hz tuning fork. After pulling her tuning valve out to slightly increase the length of her trumpet, she hears 3 beats per second against the tuning fork. Was her initial frequency 435 Hz or 445 Hz? Explain.