Four waves are produced when a harp is strummed at four different times.
| Wave 1 | Wave 2 | Wave 3 | Wave 4 |
|---|---|---|---|
| A thick, middle string is strummed at 70 dB. | A thick, middle string is strummed at 26 dB. | The long, thin string on one end of the harp is strummed at 20 dB. | The short, thin string on one end of the harp is strummed at 56 dB. |
Which wave will produce the highest pitch?
A. Wave 1
B. Wave 2
C. Wave 3
D. Wave 4
Answer (2)
The wave that will produce the highest pitch is Wave 4, as it uses a short, thin string. Shorter strings produce higher pitches compared to longer strings. Therefore, Wave 4 will have the highest pitch among the four waves provided.
;
The pitch of a string depends on its thickness and length. Thinner and shorter strings produce higher pitches. Comparing the four waves, Wave 4 uses the shortest and thinnest string, resulting in the highest pitch. Therefore, the answer is Wave 4.
Explanation
Understanding Pitch Factors Let's analyze the factors that determine the pitch of a stringed instrument like a harp. The primary factors are the string's thickness, length, and tension. Thicker and longer strings produce lower pitches, while thinner and shorter strings produce higher pitches. Higher tension also results in a higher pitch. In this problem, we're not given any information about the tension of the strings, so we'll assume the tension is constant across all strings.
Comparing String Characteristics Now, let's compare the four waves based on the string characteristics:
Wave 1: Thick, middle string, 70 dB
Wave 2: Thick, middle string, 26 dB
Wave 3: Long, thin string, 20 dB
Wave 4: Short, thin string, 56 dB
Waves 1 and 2 use the same type of string (thick, middle). Therefore, the difference in decibels (dB) only affects the loudness, not the pitch. Waves 3 and 4 use thin strings, which will produce higher pitches than the thick strings used in Waves 1 and 2.
Determining the Highest Pitch Comparing Wave 3 and Wave 4, Wave 3 uses a long, thin string, while Wave 4 uses a short, thin string. Since shorter strings produce higher pitches, Wave 4 will have a higher pitch than Wave 3. Therefore, Wave 4 will produce the highest pitch among the four waves.
Examples
Understanding how string properties affect pitch is crucial in music. For example, when designing a guitar, luthiers carefully select string gauges (thicknesses) and scale lengths (string lengths) to achieve the desired range of notes. Thicker strings are used for lower notes, while thinner strings are used for higher notes. Similarly, a piano uses strings of varying lengths and thicknesses to produce its wide range of pitches. This principle applies not only to stringed instruments but also to other sound-producing systems where frequency depends on physical dimensions and material properties.
