answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Leto
1 month ago
14

The G string on a guitar is 69 cm long and has a fundamental frequency of 196 Hz. A guitarist can play different notes by pushin

g the string against various frets, which changes the string's length. The third fret from the neck gives B♭ (233.08 Hz); the fourth fret gives B (246.94 Hz).
How far apart are the third and fourth frets?

Express your answer to two significant figures and include the appropriate units.
Physics
1 answer:
Keith_Richards [3.2K]1 month ago
6 0
Δd = 23 cm. When the eta string of the guitar has nodes at both ends, the resulting waves create a standing wave, which can be expressed with the following formulas: Fundamental: L = ½ λ, 1st harmonic: L = 2 ( λ / 2), 2nd harmonic: L = 3 ( λ / 2), Harmonic n: L = n λ / 2, where n is an integer. The rope's speed can be calculated using the formula v = λ f. This speed remains constant based on the tension and linear density of the rope. Now, let's determine the speed with the provided data: v = 0.69 × 196, yielding v = 135.24 m/s. Next, we will find the wavelengths for the two frequencies: λ₁ = v / f₁, which gives λ₁ = 135.24 / 233.08, equaling λ₁ = 0.58022 m; λ₂ = v / f₂ results in λ₂ = 135.24 / 246.94, consequently λ₂ = 0.54766 m. We'll substitute into the resonance equation Lₙ = n λ/2. At the third fret, m = 3, therefore L₃ = 3 × 0.58022 / 2, resulting in L₃ = 0.87033 m. For the fourth fret, m = 4, which gives L₄ = 4 × 0.54766 / 2, equating to L₄ = 1.09532 m. The distance between the two frets is Δd = L₄ – L₃, so Δd = 1.09532 - 0.87033, leading to Δd = 0.22499 m or 22.5 cm, rounded to 23 cm.
You might be interested in
A student must design an experiment to determine the relationship between the mass of an object and the resulting acceleration w
Softa [3030]

Respuesta:

D) Deslizar un objeto de masa conocida sobre una superficie rugosa, utilizando una fuerza aplicada constante que se puede medir con un sensor de fuerza. Colocar un detector de movimiento detrás del objeto para que se pueda medir su velocidad mientras se desliza por la superficie. Repetir el experimento con diferentes fuerzas aplicadas.

Explicación:

"El detector de movimiento proporcionará datos sobre la velocidad del objeto a lo largo del tiempo mientras se desliza por la fuerza aplicada. Esta información se puede usar para calcular la aceleración del objeto. El sensor de fuerza mide la fuerza aplicada al objeto, y se conoce la masa del objeto. Por lo tanto, este experimento puede usarse para entender cómo la masa del objeto se relaciona con la fuerza neta que actúa sobre él y la aceleración que experimenta."

No puede ser A, porque se necesita que la aceleración sea registrada por la gravedad.

No puede ser B, ya que la expresión velocidad constante implica que no hay fuerza neta, lo cual es fundamental para la pregunta inicial.

No puede ser C, porque el experimento es útil para determinar el coeficiente de fricción, pero no establece cómo la masa se relaciona con la aceleración.

Debido a que se está moviendo el objeto y tenemos un detector de movimiento, podemos graficar la aceleración en función del tiempo, lo que permite obtener muchos valores de aceleración, favoreciendo así la evaluación de la relación entre aceleración y masa.

4 0
2 months ago
A particle with mass 1.81×10−3 kg and a charge of 1.22×10−8 C has, at a given instant, a velocity v⃗ =(3.00×104m/s)j^. What are
ValentinkaMS [3465]

Answer:

The particle's acceleration magnitude and direction is a= 0.3296\ \hat{k}\ m/s^2

Explanation:

Given:

Mass m = 1.81\times10^{-3}\ kg

Velocity v = (3.00\times10^{4}\ m/s)j

Charge q = 1.22\times10^{-8}\ C

Magnetic field B= (1.63\hat{i}+0.980\hat{j})\ T

To find the particle’s acceleration

The formula for acceleration is

F = ma=q(v\times B)

a =\dfrac{q(v\times B)}{m}

We will calculate v\times B

v\times B=(3.00\times10^{4}\ m/s)j\times(1.63\hat{i}+0.980\hat{j})

v\times B=4.89\times10^{4}

Now, substitute all known values into the formula for acceleration

a =\dfrac{1.22\times10^{-8}\times(-4.89\times10^{4}\hat{k})}{1.81\times10^{-3}}

a= -0.3296\ \hat{k}\ m/s^2

The negative sign indicates the direction is opposite.

Thus, the particle’s acceleration magnitude and direction is a= 0.3296\ \hat{k}\ m/s^2

7 0
2 months ago
Read 2 more answers
A proton (mass = 1.67 10–27 kg, charge = 1.60 10–19 C) moves from point A to point B under the influence of an electrostatic for
serg [3582]

Answer:

20.353125 V

Explanation:

m = Mass of proton = 1.67\times 10^{-27}\ kg

q = Charge of proton = 1.6\times 10^{-19}\ C

v_A = Velocity of proton at point A = 50 km/s

v_B = Velocity of proton at point B = 80 km/s

The relationship derived from energy conservation is as follows:

\dfrac{1}{2}m(v_B^2-v_A^2)=q(V_B-V_A)\\\Rightarrow V_B-V_A=\dfrac{1}{2q}m(v_B^2-v_A^2)\\\Rightarrow V_B-V_A=\dfrac{1}{2\times 1.6\times 10^{-19}}\times 1.67\times 10^{-27}(80000^2-50000^2)\\\Rightarrow V_B-V_A=20.353125\ V

The determined potential difference is 20.353125 V

3 0
2 months ago
A team of engineering students is testing their newly designed raft in the pool where the diving team practices.
Yuliya22 [3333]

Answer:

Lower than

Explanation:

When the cube is placed on the raft, the displaced water equals the combined weight of both the cube and raft. In contrast, when submerged in water, the displaced water corresponds to the raft's weight plus the cube's volume. Since the cube's volume is smaller than what is needed to displace its weight with water, the water level is lower.

6 0
3 months ago
Other questions:
  • A 248-g piece of copper is dropped into 390 mL of water at 22.6 °C. The final temperature of the water was measured as 39.9 °C.
    10·1 answer
  • Sitting in a second-story apartment, a physicist notices a ball moving straight upward just outside her window. The ball is visi
    7·1 answer
  • A Styrofoam slab has thickness h and density ρs. When a swimmer of mass m is resting on it, the slab floats in fresh water with
    5·1 answer
  • Find the change in volume for a metallic dental filling due to the difference between body temperature (37.0°C) and the temperat
    15·1 answer
  • Write a hypothesis about the effect of the racetrack’s height on the speed of the car using the format of "if…then…because….” Be
    11·3 answers
  • Eac of the two Straight Parallel Lines Each of two very long, straight, parallel lines carries a positive charge of 24.00 m C/m.
    9·1 answer
  • A Top Fuel Dragster initially at rest undergoes an average acceleration of 39 m/s2 for 3.97 seconds. How far will it go in this
    15·1 answer
  • A rear window defroster consists of a long, flat wire bonded to the inside surface of the window. When current passes through th
    5·2 answers
  • Your friend states in a report that the average time required to circle a 1.5-mi track was 65.414 s. This was measured by timing
    15·1 answer
  • Suppose you are talking by interplanetary telephone to your friend, who lives on the Moon. He tells you that he has just won a n
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!